IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND … · 2018. 8. 29. · 150 IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, VOL. 65, NO. 2, FEBRUARY

IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, VOL. 65, NO. 2, FEBRUARY 2018 149

Improved Super-Resolution Ultrasound MicrovesselImaging With Spatiotemporal Nonlocal Means

Filtering and Bipartite Graph-BasedMicrobubble Tracking

Pengfei Song , Member, IEEE, Joshua D. Trzasko, Senior Member, IEEE,Armando Manduca, Member, IEEE, Runqing Huang, Ramanathan Kadirvel,

David F. Kallmes, and Shigao Chen, Senior Member, IEEE

Abstract— Super-resolution ultrasound microvessel imagingwith contrast microbubbles has recently been proposed bymultiple studies, demonstrating outstanding resolution with highpotential for clinical applications. This paper aims at addressingthe potential noise issue in in vivo human super-resolution imag-ing with ultrafast plane-wave imaging. The rich spatiotemporalinformation provided by ultrafast imaging presents features thatallow microbubble signals to be separated from backgroundnoise. In addition, the high-frame-rate recording of microbubbledata enables the implementation of robust tracking algorithmscommonly used in particle tracking velocimetry. In this paper,we applied the nonlocal means (NLM) denoising filter on thespatiotemporal domain of the microbubble data to preservethe microbubble tracks caused by microbubble movement andsuppress random background noise. We then implemented abipartite graph-based pairing method with the use of persistencecontrol to further improve the microbubble signal quality andmicrobubble tracking fidelity. In an in vivo rabbit kidney perfu-sion study, the NLM filter showed effective noise rejection andsubstantially improved microbubble localization. The bipartitegraph pairing and persistence control demonstrated furthernoise reduction, improved microvessel delineation, and a moreconsistent microvessel blood flow speed measurement. With theproposed methods and freehand scanning on a free-breathingrabbit, a single microvessel cross-sectional profile with full-widthat half-maximum of 57 µm could be imaged at approximately2-cm depth (ultrasound transmit center frequency = 8 MHz,theoretical spatial resolution ∼200 µm). Cortical microvesselsthat are 76 µm apart can also be clearly separated. These resultssuggest that the proposed methods have good potential in facili-tating robust in vivo clinical super-resolution microvessel imaging.

Index Terms— Bipartite graph, contrast microbubbles,microbubble tracking, microvessel imaging, nonlocal means(NLM) filtering, super-resolution imaging.

Manuscript received August 11, 2017; accepted November 28, 2017. Date ofpublication December 1, 2017; date of current version January 26, 2018. Thiswork was supported in part by the National Cancer Institute of the NationalInstitutes of Health under Award K99CA214523 and in part by the GeneralElectric Healthcare. The content is solely the responsibility of the authors anddoes not necessarily represent the official views of the National Institutes ofHealth. (Corresponding author: Shigao Chen.)

P. Song, J. D. Trzasko, R. Kadirvel, D. F. Kallmes, and S. Chen are withthe Department of Radiology, Mayo Clinic College of Medicine, Rochester,MN 55905 USA (e-mail: [email protected]).

A. Manduca is with the Department of Physiology and Biomedical Engi-neering, Mayo Clinic College of Medicine, Rochester, MN 55905 USA.

R. Huang is with the Division of Cardiovascular Diseases, Mayo ClinicCollege of Medicine, Rochester, MN 55905 USA.

Digital Object Identifier 10.1109/TUFFC.2017.2778941

I. INTRODUCTION

THE use of ultrasound contrast microbubbles to breakthe diffraction limit of ultrasound and realize super-

resolved microvessel imaging has recently been demon-strated in multiple studies [1]–[8]. Among these studies,Errico et al. [1] proposed a seminal method, ultrasoundlocalization microscopy (ULM), that uses ultrafast ultra-sound imaging to record spatially isolated microbubble blink-ing events from decorrelated microbubble signals that canbe generated by microbubble disruption, dissolution, andmotion. ULM achieved ∼λ/10 subwavelength spatial res-olution with a wide dynamic range of blood flow speedmeasurement (1 mm/s to several centimeters per second) that isDoppler angle independent [1], [9]. In an in vivo murine brainstudy, ULM demonstrated visualization of ∼ 10 μm microves-sels over the entire depth of the mouse brain (∼10 mm) [1].Such extraordinary combination of resolution and penetra-tion and the accurate hemodynamics measurement provides aparadigm-shifting tool for structural and functional evaluationof tissue microvasculature.

Translating super-resolution microvessel imaging tech-niques such as ULM from preclinical to clinical applicationshas great potential of providing new imaging biomarkers forearly detection, diagnosis, and prognosis of many diseases.In vivo human imaging, however, can be more challenging thanmurine brain imaging. For example, in murine brain imaging,the targeted tissue is shallow, the animal is sedated, the trans-ducer is fixed, and data accumulation for as long as 150 sand 18 bolus injections of microbubbles is achievable [1].For in vivo human imaging, on the other hand, the targetedtissue can be much deeper [which results in ultrasoundsignals with lower signal-to-noise-ratio (SNR)], physiologicand operator-induced motion is inevitable (thus, reducing theavailable data accumulation time), and significantly fewerbolus injections (typically 2–5) can be performed [10].These potential challenges demand substantial technicaldevelopment of the super-resolution microvessel imagingtechniques and need to be addressed before a successfulclinical translation can occur.

As part of the efforts to facilitate clinical translation, thispaper focused on the low SNR issue, which is frequently

0885-3010 © 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See ht.tp://ww.w.ieee.org/publications_standards/publications/rights/index.html for more information.

https://orcid.org/0000-0002-9103-6345

150 IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, VOL. 65, NO. 2, FEBRUARY 2018

observed in in vivo human imaging. The common under-lying principle of super-resolution microvessel imaging isto localize the center locations of the microbubbles andtrack the microbubble movement to derive the blood flowspeed [1]–[3], [7]. When the microbubble signal SNR is low(e.g., noise from ultrasound attenuation, thermal noise, residualtissue clutter, etc. is high), it can be challenging to differentiatethe isolated microbubble signal from ultrasound noise. Thisresults in unreliable microbubble localization, accumulation,and tracking [2], [5]. This issue may be worse for ultrafastplane-wave imaging-based super-resolution imaging becausethe unfocused plane waves typically have poorer penetrationand lower SNR than conventional focused waves, unless avery large number of angular spatial compounding frames areused (which can be inadequate for microbubble tracking dueto significantly decreased frame rate) [11]. On the other hand,the ultrafast plane-wave data acquisition offers rich spatiotem-poral information that can be advantageous for microbubbledetection and tracking. In this paper, we take advantage oftwo properties of ultrafast imaging to improve the microbubblelocalization and tracking as follows.

1) The high-frame-rate recording of the microbubble signalprovides unique microbubble movement “tracks” thatcan be observed in the spatiotemporal domain, whichprovides a strong feature that can be used to differentiatemicrobubble signals from noise.

2) The high-frame-rate imaging results in highly spatiotem-porally coherent microbubble signals from frame toframe, which provides an opportunity to use establishedglobal tracking algorithms as commonly used in parti-cle tracking velocimetry (PTV) for robust microbubbletracking.

Specifically, for the first point, we propose to implement thenonlocal means (NLM) denoising filter [12] on the spatiotem-poral microbubble data to suppress the background noise andextract the microbubble movement tracks, and for the secondpoint, we propose to use a two-frame PTV tracking methodbased on minimum distance bipartite graph pairing [13], [14]to realize efficient and robust microbubble tracking.

To obtain a more realistic imaging environment and amicrobubble data set more representative of what is expectedin humans, in this paper, we used an in vivo rabbit kidneymodel with freehand scanning to test the proposed methods.Using an in vivo setup also eases the burdens of creating aproper in vitro imaging model (e.g., simulated or phantomdata) with the appropriate noise characteristics, which is nottrivial and requires additional investigation. Nevertheless, thisin vivo experimental setup allows convenient comparisonsbefore and after the application of the proposed methods onthe same set of reference data, which is appropriate for thepurpose of demonstrating the effectiveness of the introducedmethods.

The rest of this paper is organized as follows. In Section II,we briefly introduce the animal preparation and key stepsof microbubble super-resolution imaging, and then focuson introducing the details of the spatiotemporal NLMdenoising method and the bipartite graph microbubble pair-ing and tracking method. We then show results of the

improvement achieved by each method together with the finalsuper-resolved microvessel perfusion image and microvesselblood flow speed image. Finally, we provide discussion andconclusions.

II. MATERIALS AND METHOD

A. In Vivo Rabbit Study Setup

The testing microbubble data set was obtained from afemale New Zealand white rabbit. The experiment conformedto the policy of the Institutional Animal Care and Use Com-mittee at Mayo Clinic. The rabbit was anesthetized with keta-mine (35.0 mg/kg) and xylazine (6.0 mg/kg). The right kidneyof the rabbit was imaged. For ultrasound data acquisition,a Verasonics Vantage system (Verasonics Inc., Kirkland, WA,USA) and a linear array transducer L11-4v (Verasonics Inc.,Kirkland, WA, USA) were used. A five-angle (−4° to 4° witha step size of 2°) plane-wave compounding with effectivepulse repetition frequency (PRF) of 500 Hz was used (centerfrequency = 8 MHz). The mechanical index of the transmitpulse was 0.4 [1]. The spatial resolution of the ultrasound datawas 0.172 mm. A total of 1000 ensembles were acquired (cor-responding to 2-s time duration), with 200 ensembles(0.4-s time duration) acquired in each second (total dataacquisition time = 5 s). The rabbit was allowed to have freebreathing and freehand scanning was conducted. The imagingfield of view (FOV) was carefully chosen so that only in-planekidney motion caused by breathing was observed (i.e., no out-of-plane tissue motion). Before data acquisition, a 0.1 mL(5.0–8.0 × 108 microspheres per milliliter) bolus injection ofOptison (GE Healthcare, Milwaukee, WI, USA) suspensionwas administered through the marginal ear vein followed by a1-mL flush of saline. Ultrasound data acquisition started afterthe kidney was fully perfused by microbubbles.

B. Processing Steps for Super-Resolution Imaging

Fig. 1 summarizes the key processing steps for super-resolution imaging. A 2-D phase-correlation-based rigidgeometric image registration method (the “imregcorr.m”function in MATLAB) was used to first remove the in-planetissue motion caused by breathing. The blinking microbubblesignal (caused by microbubble movement, disruption,and dissolution) was then extracted by a subtraction ofimmediately adjacent frames (i.e., frame to frame) of thein-phase quadrature data [1], which removes the backgroundtissue signal and constant microbubble signals. The ultrasounddata before and after the frame-to-frame subtraction are shownin Fig. 2(a) and (b), respectively. The extracted blinkingmicrobubble signal was then passed down to the rest of theprocessing chain.

C. Spatiotemporal Nonlocal Means (NLM)Denoising Filtering

After frame-to-frame subtraction, the blinking microbubblesignal is more clearly revealed [Fig. 2(b)]. However, one canalso easily appreciate the ultrasound noise that resembles themicrobubble signal, for example, the locations indicated by the

SONG et al.: IMPROVED SUPER-RESOLUTION ULTRASOUND MICROVESSEL IMAGING 151

Fig. 1. Processing steps of microvessel super-resolution imaging.

Fig. 2. Ultrasound amplitude image (B-mode). (a) Before frame-to-frame subtraction. (b) After frame-to-frame subtraction. (c) After spatiotemporal NLMdenoising filtering. The red vertical line in (b) indicates the location from which the spatiotemporal data example in (d) was obtained. The green arrowsin (b) indicate example locations where the NLM denoising effect can be well appreciated. (d) Spatiotemporal data extracted from (b), with one dimensioncorresponding to the axial direction z of the ultrasound data, and the other dimension corresponding to time t . The green solid box indicates the targetedpixel, the green box indicates the patch centered on the targeted pixel, the red solid box indicates a nonlocal pixel, the red box indicates the patch centeredon the nonlocal pixel, and the yellow box indicates the search window. (e) NLM filtered result of (d). (f) Difference image between (d) and (e). Movies of

the before and after spatiotemporal NLM filtering results (Supplemental videos 1 and 2 , respectively) are available in supplemental materials.

green arrows in Fig. 2(b). Since microbubble localization relieson recognition of patterns that resemble the ultrasound systempoint spread function (PSF), these noise signals can be falselyidentified as microbubbles. A 2-D spatial smoothing filtercombined with amplitude thresholding (i.e., rejection of imageintensities values lower than a certain threshold) can alleviatethe noise issue. However, this may not work in regionswhere the noise has amplitude comparable to the microbubblesignal, and spatial smoothing filters may merge the origi-nally isolated microbubbles, undermining the super-resolutioncapability. From an image processing perspective, it is verychallenging to separate the microbubble signal from noisebased only on the spatial information provided in Fig. 2(b).Therefore, we propose to add the temporal dimension into

the processing and consider denoising the microbubble signalin a spatiotemporal domain. Fig. 2(d)–(f) shows such anexample. In Fig. 2(d), one can clearly discern the microbub-ble “tracks” resulting from microbubble movement with theblood flow in the spatiotemporal domain (axial dimension andtemporal dimension), as opposed to the random backgroundnoise that does not resemble any feature or pattern. Thisdistinct feature of the microbubble signal in the spatiotemporaldomain allows more robust denoising. In this paper, we usedthe established NLM filter for the denoising task, to bestpreserve the microbubble track features and suppress noisewithout significant blurring (a key characteristic of NLM fil-tering). The detailed principles of NLM filtering can be foundin [12] and [15]. Briefly, as shown in Fig. 2(d), the NLM


filter compares the intensity values between two patches ofpixels (one patch x(Ni ) centered on the targeted pixel xi

[indicated by the green box in Fig. 2(d)] and the other patchx(N j ) centered on another pixel x j that is a certain distanceaway [indicated by the red box in Fig. 2(d)] and replacesthe pixel value of xi with a weighted average of the pixelvalues within the search window [indicated by the yellow boxin Fig. 2(d)]. Specifically,

xi =∑

j∈I

w(i, j)x j (1)

where w(i , j) is the weight between patch i and patch j andis given by

w(i, j) = 1

Zie− �x(Ni )−x(N j )�2

2h2 (2)

where Zi is a normalization factor that ensures the sum of wis equal to unity, and h controls the amount of filtering (thehigher the h the more the smoothing). The center pixel xi isassigned with the highest weight obtained from the searchwindow I . As suggested by (2), the higher the similarityof intensity values between the targeted pixel patch andthe nonlocal patch, the higher the weight. The patch sizeN is typically determined by the size of the feature (i.e.,size of the microbubble tracks, which was chosen to be0.5 mm spatially by 20 ms temporally in this paper) and thesearch window size I was empirically chosen to be twicethe patch size. The smoothing control factor h was chosento be one standard deviation of the background noise of thespatiotemporal data. After NLM denoising filtering, as shownin Fig. 2(e) and (f), one can see the marked improvementof the signal quality thanks to the effective suppression ofbackground noise by the NLM filter. The microbubble trackswere well preserved with minimum blurring. After applyingthe NLM filter on the entire data set, one can again appreciatethe significant improvement of signal quality in Fig. 2(c),as compared Fig. 2(b). Videos of the microbubble signalsbefore and after the spatiotemporal NLM filtering are pro-vided in the supplemental materials (Supplement videos 1and 2 ).

D. Microbubble Localization

The processing used for microbubble localization isdescribed through an example, as shown in Fig. 3. TheNLM filtered microbubble signal was first thresholded byintensity value (i.e., rejecting pixels with intensity values< −40 dB (fine-tuned to this specific data set) of themaximum microbubble intensity value in each frame) tofurther suppress unreliable microbubble signal and noise. Thedata was then spatially interpolated to 0.02-mm resolutionusing 2-D linear interpolation (the “interp2.m” function inMATLAB), as shown in Fig. 3(b). A system PSF [Fig. 3(g)]was derived based on typically observed microbubble sig-nal dimensions and shape [i.e., full-width at half-maximum,Fig. 3(f)] using a multivariate Gaussian model. The PSF wasthen used to perform a 2-D normalized cross-correlation witheach frame of the interpolated microbubble signal, resulting

in 2-D cross-correlation coefficient maps [Fig. 3(c)]. Pixelswith cross-correlation coefficient less than 0.6 were thenrejected, creating isolated blobs. The peaks of each isolatedblob, representing the center location of the microbubble,were identified by searching for the regional maximum cross-correlation coefficient value (e.g., “imregionalmax.m” functionof MATLAB). The example of localization results are givenin Fig. 3(e) and (h).

E. Bipartite Graph-Based Microbubble Pairing and Tracking

Similar to PTV where high-speed cameras capture themotion of flow particles, super-resolution microvessel imaginguses high-frame-rate ultrasound to capture the flow motionof microbubbles. Because of the high-frame-rate recording,the most likely position that the same target (i.e., parti-cles or microbubbles) in frame n will appear in frame n + 1is the location that is closest to where the said target wasin frame n. Therefore, by pairing targets between consecutiveframes in a bipartite graph fashion with the goal of minimizingtotal pairing distance, the targets can be robustly tracked [13].Here, we use the examples shown in Fig. 4 and the detailedflowchart of the pairing algorithm in Fig. 5 to explain thepairing and tracking method. As shown in Fig. 4(a), the dis-tance between each possible pair of microbubble locationsin adjacent frames is first calculated to form a 2-D matrix.A physiological blood flow speed limit of 50 cm/s wasapplied to the distance matrix, rejecting cases of microbubblemovement greater than 1 mm with a 2-ms time intervalbetween two consecutive frames [Fig. 2(b)]. Mutually pairingeach microbubble in frame n and each microbubble in framen + 1 with a minimum total distance can be solved by theclassic Hungarian algorithm for assignment problems (a.k.a.Kuhn–Munkres algorithm) [16], [17]. However, due to theexistence of false microbubble signals resulting from noise andother microbubble events (e.g., disappearance of microbub-ble signal or emergence of new microbubble signal), somemicrobubble signals cannot (and should not) be paired. Stan-dard formulations of the Hungarian algorithm require that alltargets in at least one of the frames (the frame with the smallernumber of targets) be paired, and this can give a suboptimalresult in our situation. Here, we developed a partial assignmentalgorithm for bipartite graph pairing which does not requireall targets to be paired. The detailed algorithm is presentedin the flowchart in Fig. 5. Briefly, the algorithm enforces thatthe pairing distance has to be mutually minimal for the pairedmicrobubbles. If a microbubble in frame n has exhausted itspairing options in frame n + 1 and still cannot be paired,then this microbubble signal will be discarded. The pairingdistance and direction were recorded to track microbubblemovement from frame to frame. Fig. 4(c) shows an exampleof microbubble locations in two consecutive frames n andn + 1, and Fig. 4(d) shows the pairing result with trackedmicrobubble movement between the same two frames. Onecan see that some microbubbles in frame n could not find apaired microbubble in frame n + 1, and were consequentlydiscarded.

To facilitate more robust microbubble tracking, a persis-tence control can be conveniently adapted for the proposed


Fig. 3. Processes of microbubble localization. (a) Example of a local region of the microbubble data, followed by (b) 2-D spatial interpolation, normalized(c) 2-D cross-correlation with the derived system PSF, (d) cross-correlation coefficient thresholding, and finally identifying microbubble center locations bysearching local maximum correlation coefficient. (e) Example of the localization indicated by the red crosses. (f) Zoomed-in-view image of a microbubblesignal. (g) Derived PSF signal based on (f). (h) Example of the microbubble localization result on the full FOV data.

pairing method. The persistence control requires that the samemicrobubbles be paired in P consecutive frames (excludingthe current frame where the targeted microbubble is in) tobe counted as a reliable microbubble signal, which can thenbe used in final super-resolution accumulation and bloodflow speed calculation. As an example, for P = 3, thesame microbubbles have to be paired between frames n andn + 1, n + 1 and n + 2, and n + 2 and n + 3. The pathof the microbubble movement was recorded and each timea microbubble propagated through a pixel, the pixel valuewas increased by 1. The final super-resolution microvessel

perfusion map was constructed from this microbubble counterresult. The super-resolution microvessel blood flow speed mapwas obtained by calculating blood flow speed v at each spatiallocation (i , j)

v(i, j) = 1

C

C∑

k=1

v(i, j)k

v(i, j)k = �d

T(3)

where C is the total number of times a microbubble appearedat pixel (i , j), T is the time duration between consecutive


Fig. 4. (a) Distance matrix obtained by calculating the movement distance between all possible pairings of microbubbles from frame n to frame n + 1. Theaxes indicate the indices of the microbubble locations. (b) Thresholded distance matrix using a blood flow speed limit of 50 cm/s. (c) Microbubble locationsin frames n and n + 1. (d) Bipartite graph tracking result. The blue arrows indicate the distance and direction of microbubble movement between consecutiveframes.

frames (i.e., 1/PRF), and �d is the microbubble movementdistance between consecutive frames. To improve robustnessof �d estimation, a cumulative sum ds was calculated fromeach �dn obtained from P consecutive frames

ds =s∑

n=1

�dn, s ≤ P . (4)

Then, a linear fit was performed on ds , and a new stepmicrobubble movement �d � can be calculated by

�d � = ∂ds/∂s (5)

where �d � was finally used in (3) to calculate microbubbleflow speed.

III. RESULTS

A. Spatiotemporal NLM Filtering Results

Fig. 6 shows one frame of microbubble localization resultsusing the microbubble signal that is not filtered [Fig. 6(a)],filtered with a 2-D spatial Gaussian smoothing filter (kernelsize = 0.86 mm, σ = 1), and the proposed spatiotempo-ral NLM filter. The impact of noise on microbubble local-ization is clearly demonstrated in these examples. Withoutfiltering, many false microbubbles are localized. While the2-D Gaussian filter alleviates the noise, it significantly blursthe microbubble signal and results in cases where isolated

microbubble sources could not be resolved [examples shownby the green arrows in Fig. 6(b) and (c)]. Meanwhile, a sub-stantial amount of noise is still misidentified as microbubbleswith 2-D Gaussian filtering (e.g., the medulla region inside thekidney and the area below the kidney). Spatiotemporal NLMfiltering, on the other hand, did not blur the microbubble signaland robustly rejected most of the noise signal.

The improvement brought by the spatiotemporal NLM filtercan be further illustrated in Fig. 7, which shows the accumu-lated super-resolution microvessel perfusion images obtainedfrom various filtering options as in Fig. 6 (to facilitate a bettervisualization of the microvessel structure and improvement,only local regions of the kidney are shown in the comparisonresults hereinafter). One can appreciate the impact of noisewhen no filtering is applied. A similar microvascular structurecould be observed among the three filtered results, but theNLM filtered result has the least amount of noise and showsmarked improvement of delineation of the super-resolvedmicrovessels.

B. Bipartite Graph Pairing Results

Fig. 8 shows example results of microbubble pairing byusing the Hungarian algorithm [17] (Fig. 8(b), source codeavailable from [18]) and the proposed partial assignmentalgorithm [Fig. 8(c)]. Similar pairing results were obtainedfor both algorithms, except for the central portion of the data.


Fig. 5. Flowchart of the partial assignment pairing algorithm based on bipartite graph with minimum pairing distance.

Fig. 6. (a) Microbubble localization (red dots) using the microbubble signal without any filtering. (b) 2-D spatial Gaussian smooth filtering. (c) Proposedspatiotemporal NLM denoising filtering.

As marked by the white dashed lines in Fig. 8(b), the Hun-garian algorithm had two pairs of microbubbles (one in framen close to the microbubble index number 240 and the other

one in frame n + 1 close to the microbubble index number187) that were left unpaired (i.e., no intersections with anyavailable distance dots) by the partial assignment algorithm.


Fig. 7. Accumulated local super-resolution microvessel perfusion images (compressed by taking the square root of the original data for better visualization)obtained with the microbubble signal (a) without any filtering, (b) 2-D spatial Gaussian smooth filtering, and (c) proposed spatiotemporal NLM denoisingfiltering. All images were from the central upper cortex of the kidney.

Fig. 8. (a) Distance matrix before microbubble pairing. (b) After pairing with the Hungarian algorithm. (c) After pairing with the proposed partial assignmentalgorithm. (d) Paired distances for both pairing algorithms.

As a result, the Hungarian algorithm delivered a higher numberof pairings, but at the expense of a higher overall pairingdistance. For all the microbubbles in this example [Fig. 8(a)and (b) only shows part of the pairing distance matrix],the Hungarian algorithm paired 379 pairs of microbubbleswith a total pairing distance of 96.6 mm, while the partialassignment algorithm paired 350 pairs of microbubbles witha total pairing distance of 39.5 mm. This can be further illus-trated in Fig. 8(d), where it can be seen that for the unmatchedpairings between the two algorithms, the Hungarian algorithm

typically provides a higher pairing distance. One reason forthis behavior of the Hungarian algorithm, which was originallydesigned to solve the assignment problem with the goal ofminimizing total assignment cost, is that it provides as manypairings as possible while minimizing the pairing distances.For microbubble pairing, however, due to the existence offalse microbubble signals and the disappearance or birth ofmicrobubbles, maximizing the number of pairings may not bethe optimal solution. The proposed partial assignment algo-rithm trades-off the total number of pairings for lower pairing


Fig. 9. Accumulated microvessel super-resolution perfusion maps (compressed by taking the square root of the original data for better visualization)(a) and (c) before and (b) and (d) after microbubble pairing.

distances and allows for discarding microbubbles that cannotbe paired. The final accumulated super-resolution microvesselperfusion images before and after pairing with the proposedpartial assignment algorithm are shown in Fig. 9. It can beseen that the pairing process—and the discarding of signalsthat could not be paired—gave rise to a further reductionof unreliable microbubble signals and noise (example regionsindicated by white arrows), especially for the lower cortex ofthe kidney with relatively low microbubble SNR.

C. Persistence Controlled Pairing and Tracking Results

Fig. 10 shows the accumulated super-resolution microvesselimages with different persistence control settings. The imageswithout persistence control are the same as the post-pairingresults shown in Fig. 9. From Fig. 10, one can see that persis-tence control further reduces noise and enhances microvesselswith persistent microbubble signals that can be tracked formultiple frames (example regions indicated by white arrows).Similar to the observation in Fig. 9, the improvement ismore significant for the lower cortex of the kidney. Thehigher the persistence control factor the higher the fidelityof microbubble tracking. However, the higher constraint ofmultiframe tracking from the high persistence control mayalso eliminate real microvessels and results in a less detailedmicrovascular image [e.g., Figs. 10(c) and (d)]. As shownin Fig. 10, a persistence control factor of 5 (i.e., the samemicrobubble has to be tracked continuously within a 10-ms

time interval) empirically provides a good tradeoff betweennoise reduction and microvessel visualization. In this data set,a total number of approximately 1.1×105 microbubble eventswere detected after the NLM denoising and microbubble local-ization processes. After the pairing and persistence controlsteps, ∼ 0.6×105 microbubble events were preserved and usedto construct the final microvessel perfusion and flow speedmaps.

To effectively alleviate the sparse and pixelated appearanceof the super-resolved microvessel images without introduc-ing blurring, a local weighted average algorithm proposedin [3] can be implemented. Briefly, for a nonzero localwindow (i.e., regions for which at least one microbubblepropagated through), the center pixel value is replaced by adistance-weighted average of all nonzero pixel values withinthis local window. In this paper, a 3×3(0.06 mm×0.06 mm)local window was used for weighted averaging. Fig. 11 showsthe final weighted average result of the P = 5 persistencecontrolled microvessel image. At approximately 2-cm depth,a single microvessel cross-sectional profile with full widthat half maximum of 57 μm could be imaged. Microvesselsthat are 76 μm apart can also be clearly separated. Althoughone can clearly observe the larger vessels (e.g., vessels largerthan arterioles) in Fig. 11, multiple microbubble passages maybe necessary to robustly measure their dimensions. A movieshowing the dynamic super-resolved microvessel accumulationprocess can be found in Supplemental video 3 .


Fig. 10. Accumulated local microvessel super-resolution perfusion maps (compressed by taking the square root of the original data for better visualization)(a) and (d) without persistence control, (b) and (e) with persistence control P = 5 which corresponds to 10 ms of multiframe tracking, and (c) and (f) withpersistence control P = 10 which corresponds to 20 ms of tracking.

The improvement from the persistence control method canbe further illustrated by the microvessel blood flow speed mapsin Fig. 12. All the blood flow speed maps were processed withthe local weighted average method. The blood flow directionwas color-coded with blue corresponding to blood flow towardthe transducer and red corresponding to flow away from thetransducer. The blood flow speed measurement distributionsof the local upper cortex and lower cortex of the kidneyas in Fig. 12 are shown as histograms in Fig. 13. FromFig. 12, one can see that similar to the observations from themicrovessel perfusion images, persistence control was effec-tive in suppressing the noise and providing a better delineationof the microvessels. Fig. 13 shows a narrower blood flowspeed distribution with a higher persistence control factor,which indicates that a more uniform and consistent bloodflow speed measurement could be achieved with persistencecontrol. Similar to the observations above, the improvementis more pronounced for the lower cortex of the kidney wherethe microbubble SNR is relatively low.

D. Comparisons With the Hungarian Algorithm-BasedTracking and Cross-Correlation-Based LocalMicrobubble Tracking Methods

Figs. 14 and 15 further demonstrate the effectiveness of thespatiotemporal NLM denoising filter in facilitating more robustmicrobubble tracking by suppressing noise. Figs. 14 and 15also demonstrated comparisons among different tracking meth-ods that include the cross-correlation-based local microbubbletracking technique similar to the ones used in [1] and [3],

the Hungarian algorithm, and the proposed partial assignmentalgorithm. Both Hungarian and partial assignment methodsused a blood flow speed limit of 50 cm/s. All tracking methodsused the same microbubble localization signals. For cross-correlation-based local tracking, a 42- by 62-μm (axial bylateral) local window (about the size of a single microbubblePSF) centered on the microbubble peak was used to search inan 82- by 122-μm search window in adjacent frames by useof 2-D normalized cross-correlation. Microbubble movementwas estimated by locating the peak of the normalized cross-correlation coefficient. For all tracking methods, a persistencecontrol of five frames was used to reject unreliable microbub-ble signals. As shown in Figs. 14 and 15, all tracking methodsshowed substantially improved results after the spatiotemporalNLM filtering. There was significantly less noise in themicrovessel density maps as well as the blood flow speedmaps with the NLM denoising filter. Among various trackingmethods, the proposed partial assignment algorithm showedimproved results over the Hungarian algorithm both with andwithout the NLM filter (green arrows in Fig. 14), especiallyfor the flow speed estimates. This can be attributed to the morerobust microbubble pairing by the proposed partial assignmentalgorithm as illustrated in Fig. 8. Cross-correlation-based localtracking showed similar performance as the partial assignmentalgorithm. This is expected because as shown in Supplemen-tal video 2 , the microbubble density in this paper waslow and thus it was straightforward to use the local cross-correlation-based approach for bubble tracking. In cases wheremicrobubble density is high or microvessel morphology is


Fig. 11. Super-resolution microvessel perfusion images processed with the local weighted averaging method. Three regions of the original microvessel image

were magnified to show the detailed microvasculature. The dynamic microvessel accumulation process can be found in Supplemental video 3 . A branchingmicrovessel at about 2-cm depth was located to measure the microvessel cross-sectional profile (bottom).

more complicated, a more elegant local tracking method suchas the Markov chain-based tracking algorithm proposed in [2]may be necessary. Table I summarizes the computational costof the NLM denoising filter and each tracking algorithm.Both Hungarian and partial assignment algorithms are signifi-cantly cheaper than the cross-correlation-based local tracking

method. This is because both Hungarian and partial assignmentmethods converted the tracking problem to a much simplertask of finding the track in a 2-D distance matrix [Fig. 4(b)]that gives minimal total pairing distance. Computationally, thisis much less intensive than normalized cross-correlation-basedsearching for each individual microbubble.


Fig. 12. Super-resolution microvessel blood flow speed maps obtained from different amounts of persistence control. (a) No persistence control. (b) Persistencecontrolled (P = 5). (c) Persistence controlled (P = 10). The left column shows the global result and the right column shows the magnified local regionsin the upper kidney cortex (top) and lower kidney cortex (bottom). All blood flow speed maps are under the same scale indicated by the color bar. Flowdirection toward the ultrasound transducer was color-coded in blue, and away from the transducer was color-coded in red.

TABLE I

COMPUTATIONAL TIME ASSOCIATED WITH NLM FILTERINGAND DIFFERENT TRACKING METHODS

IV. DISCUSSION

In this paper, we proposed two methods to take advantageof the rich spatiotemporal information of ultrafast plane-wave

imaging data, with the objectives of improving microbubblelocalization and tracking to improve the overall robustness ofsuper-resolution microvessel imaging. The first method appliedthe NLM denoising filter on the spatiotemporal microbubblesignal to effectively suppress the decorrelated backgroundultrasound noise by preserving the coherent microbubblemovement tracks. The second method uses the principles ofbipartite graph pairing to robustly track microbubble motionby minimizing the global pairing distances while allowingfor the presence of signals that should not be paired. Eachstep of the two methods showed significant reduction in noiseand enhanced microvessel image quality in an in vivo rabbit


Fig. 13. Histograms showing blood flow speed measurement distributions with different persistence control settings. (a) Upper cortex of the kidney.(b) Lower cortex of the kidney. The same regions of the upper and lower cortex as in Fig. 12 were used to generate the histograms.

kidney data set. A final super-resolution microvessel imagewas generated in which microvessels as small as 57 μm in full-width at half-maximum could be discerned and 76 μm apartcould be separated at 2-cm depth, together with quantitativeDoppler-angle independent blood flow speed measurementsfor each microvessel.

An NLM denoising filter has been previously used inultrasound B-mode imaging and showed superior performancein preserving the ultrasound image features without blurringwhile achieving substantial speckle reduction [12]. Simi-lar to the speckle reduction application, the spatiotemporalmicrobubble data also presents strong features from microbub-ble movement while background noise is random and redun-dant. This provides an ideal situation for the NLM denoisingfilter. Fig. 16(b) shows an example of implementing the NLMdenoising filter solely on the spatial domain (i.e., axial andlateral dimensions) of the microbubble data [i.e., to denoiseFig. 2(b)], as opposed to spatiotemporal filtering. One cansee that the spatial NLM filter could not provide as robustdenoising as the spatiotemporal NLM filter, especially forthe lower left region of the kidney cortex (indicated by thewhite arrows). This is because with spatiotemporal filtering,the microbubble behavior over time provides strong featuresthat allow the NLM to perform well. In this paper, the spa-tiotemporal microbubble data was extracted from the axial-temporal domain of the ultrasound data (i.e., the NLM filterwas performed on 2-D microbubble data with one dimensionin axial dimension and the other dimension in temporal dimen-sion). An alternative spatiotemporal data can be extractedfrom the lateral-temporal domain, and the NLM filtered resultis shown in Fig. 16(c). While the lateral-temporal filteringprovides slightly better denoising result than spatial NLMfiltering [Fig. 16(b)], it is still not as good as the axial-temporal NLM filter. The microbubbles are also better isolated(e.g., region indicated by red arrows) by using the axial-temporal data. One potential reason for the better performanceof axial-temporal filter in this paper is that kidney bloodflow direction is primarily along the axial direction (Sup-plemental videos 1 and 2 ), which provides a stronger

microbubble movement feature that facilitates a more robustNLM denoising. Theoretically, a 3-D NLM filter (two dimen-sions in space and one dimension in time) should be able toaccount for the different microbubble movement directions.However, 3-D NLM filter can be very computationally expen-sive for the large ultrafast ultrasound data size. Future studiesneed to be conducted to fully investigate the feasibility of using3-D NLM filters for microbubble signal denoising.

The patch size selection of the NLM denoising filter hasa significant impact on microbubble signal denoising andcomputational cost: larger patch sizes tend to smooth out morefeatures (i.e., bubble tracks) and are more computationallyexpensive, while smaller patch sizes tend to preserve morefeatures and are faster to compute. This can be illustratedin Fig. 17, which shows the effect of NLM denoising usingdifferent sized patches (indicate by the red boxes). Thepatch size of 0.5 mm by 20 ms was used in this paper toachieve optimal denoising without suppressing microbubblesignals.

Unlike local microbubble tracking techniques (such as thecross-correlation-based method showed in this paper) wherea local search window is typically used to locally monitorthe microbubble movement, the bipartite graph pairing andtracking algorithm tracks microbubble movement on a globalscale. The basic principle of this tracking method, similarto the case in PTV, is that under high speed tracking themost likely position in which a microbubble will appear inthe next frame is in the close vicinity of its position in thecurrent frame. This can be demonstrated in the microbubblesignal movie in Supplemental video 1 . Another advantageof the global tracking method is that all possible pairings areconsidered simultaneously between two consecutive framesin the form of a pairing distance matrix, and the task ofpairing and tracking is condensed into a simple 2-D matrix[see Fig. 4(b)] by minimizing the global pairing distances. Thisavoids the use of computationally expensive local trackingmethods such as 2-D cross-correlation (Table I) and the needto establish complicated models to track a large number ofmicrobubbles simultaneously.


Fig. 14. Microvessel density images processed with various combinations of filtering and tracking methods. Right column images were all denoised withthe spatiotemporal NLM filter, and the left column images were not. The corresponding pairing and tracking algorithms are listed on the left side of eachrow. All density images are displayed under the same scale, which was intentionally set to make the images saturated in order to better illustrate the noisedifferences among different methods.

This paper aimed at addressing the potential low SNR issuewhen performing super-resolution microvessel imaging inhuman. As mentioned in the introduction, there are many otherpotential technical challenges of the super-resolution imagingtechnique. For example, in this paper, a basic phase-correlationimage registration method was used to remove the global tissuemotion caused by breathing. Recently, a fine-tuned phase-correlation-based rigid-motion correction method designatedfor ULM has been proposed [19]. These methods may beacceptable for motions similar to the kidney motion observedin this paper which was mostly global (i.e., the entire kid-ney moves together) and translational. For more complicated

nonrigid tissue motion a more robust registration method maybe necessary. In addition, in this paper, a simulated ultrasoundsystem PSF was used to localize the microbubble location. ThePSF was simulated based on measuring the typical microbub-ble dimensions and shapes (e.g., full-width at half-maximum)observed in the rabbit kidney data. In practice, the ultrasoundPSF is not spatially invariant and can be affected by con-founding factors such as phase aberration, reverberation, andother noise. The PSF may also be different among differentimaging systems and imaging applications. A more advanceddeconvolution method such as blind deconvolution may bemore reliable in localizing the microbubbles. Nevertheless,


Fig. 15. Microvessel blood flow speed images processed with various combinations of filtering and tracking methods. Right column images were all denoisedwith the spatiotemporal NLM filter, and the left column images were not. The corresponding pairing and tracking algorithms are listed on the left side ofeach row. All flow speed maps are displayed under the same scale.

the proposed NLM filtering and microbubble pairing methodscan improve upon these techniques and increase the overallrobustness of super-resolution imaging.

The theoretical resolution limit of the super-resolution imag-ing sequence used in this paper can be calculated followingthe theories proposed in [1], where the axial resolution limitis given by the axial localization error σz ≈ cστ /(2(n)1/2)(c is the ultrasound speed, στ is the timing resolution of thesystem given by (6), and n is the number of channels usedin receive processing), and the lateral resolution limit is given

by the lateral localization error σx ≈ 2(3)1/2cστ f/(D(n)1/2)( f is the focal length and D is the transducer array dimension).The timing resolution limit of the system στ is bounded bythe Cramér–Rao lower bound of the ultrasound system, whichis given by [20]

στ = σ(τ̂0 − τ0)

≥√√√√ 3

2 f 30 π2T (B3 + 12B)

(1

ρ2

(1 + 1

SNR2

)2

− 1

)(6)


Fig. 16. Microbubble images filtered by (a) spatiotemporal (axial-temporal dimension of data) NLM denoising filter, (b) spatial (axial-lateral dimensionof data) NLM denoising filter, and (c) alternative spatiotemporal NLM filter using data in lateral-temporal dimension.

Fig. 17. Effect of patch size on NLM denoising and computational time. The red box in each figure indicates the patch size. The search window size istwice the patch size in each dimension.

where f0 is the ultrasound transmit pulse center fre-quency (8 MHz), T is the kernel size for the time delayestimation (for microbubble localization, this is essentiallythe timing resolution of the raw channel RF signal, whichis equal to 28 ns in this paper), B is the bandwidth ofthe transmit pulse (conservatively estimated to be 25%), ρis the normalized correlation coefficient between the exper-imental signal and the reference PSF used for localization[the correlation cutoff threshold value of 0.6 as in Fig. 3(d)was used to be conservative], and SNR is the SNR and wasassumed to be 20 dB. στ was calculated to be 80.3 ns,which gives an axial resolution limit of 5.5 μm, and lateralresolution limit of 9.9 μm at 1-cm depth, and 19.7 μm at2-cm depth (elevational focal depth of the L11-4v transducer).The lateral resolution limit at the elevational focal depth isapproximately 1/10 of the diffraction limit of the 8-MHztransmit pulse, which is 192.5 μm. This is in good agreementwith the observations reported in [1] and [9].

In this paper, a simple and cheap frame-to-frame sub-traction method was used to reject tissue signal and extractthe blinking microbubble signal. Recently, multiple stud-ies have shown the robustness of using singular valuedecomposition (SVD)-based clutter filters for microvesseltissue clutter filtering [21]–[23]. However, as comparedto frame-to-frame subtraction, SVD-based filters can be

Fig. 18. Pairing performances of the Hungarian algorithm and the proposedpartial assignment algorithm with various blood flow speed limits as thresholdsto reject entries of the pairing distance matrix. The left axis indicates the totalpairing distance between two consecutive frames with localized microbubblesignals, and the right axis indicates the percentage of matched pairingsbetween the two algorithms.

computationally more expensive. In this paper, we found theframe-to-frame subtraction method effective in tissue signalsuppression thanks to the high-frame-rate imaging and signif-icantly improved SNR of blood signal provided by microbub-


Fig. 19. Super-resolution kidney microvessel perfusion images from the 15-s data set with 4125 frames acquired from a free-breathing rabbit with freehandscanning and a single bolus injection.

bles. In cases where blood flow speed is significantly higheror the imaging frame rate is significantly lower, however, theframe-to-frame subtraction may result in inaccurate microbub-ble peak locations. More advanced filtering techniques suchas SVD may be more appropriate for these applications.Future studies are needed to systematically investigate theimpact of different tissue rejection and microbubble extractiontechniques for super-resolution imaging.

Similar to the Hungarian algorithm, the partial assignmentalgorithm developed in this paper is based on the bipartitegraph matching theory that specifically deals with weightedbipartite graphs [24] (that is, the edges connecting vertices ofthe graph have different weights, such as the pairing distancebetween microbubbles in this paper). The Hungarian algorithmprovides optimal solutions to this kind of “max-flow, min-cost” problem (i.e., maximum matching with minimum cost)with the premise that the final matching has to be perfect(a perfect matching requires all vertices to be adjacent to someedge) [25]. This is the key difference between the Hungarianalgorithm and the proposed partial assignment approach whichdoes not require the matching to be perfect—some microbub-bles were allowed to be unpaired and discarded. Note that thepartial assignment in this paper is different from the partial

association problem in the Hungarian algorithm in which, forinstance, M workers need to be assigned to N jobs withM ≥ N , and the Hungarian algorithm will guarantee Nparings (i.e., a perfect match) while our algorithm does not(e.g., final number of parings ≤ N). This allows the proposedalgorithm to be more flexible and effective in rejecting falseand unreliable microbubble signals (Fig. 8), which is not aproblem that the Hungarian algorithm was originally designedto solve. Fig. 18 further illustrates the difference between thetwo algorithms by comparing the pairing results from the sameset of microbubble location data. One can see that the proposedpartial assignment algorithm consistently provided lower totalpairing distances than the Hungarian algorithm, except whenno blood flow speed limit was utilized [that is, using theoriginal distance matrix as in Fig. 4(a) for pairing]. Thisis expected because the Hungarian algorithm is the optimalsolution to a weighted pairing problem as in Fig. 4(a), when noa priori information about microbubble flow speed is provided.When a priori blood flow speed limit was used as thresholdsto reject unrealistic distance entries [Fig. 4 (b)], as shownin Fig. 18, both algorithms showed improved performanceswith a descending trend of pairing distances. A speed limitof 150 cm/s was sufficient to ensure robust performance of the


proposed algorithm, which is a very relaxed constraint becausethe upper bound of physiological range of normal blood flowspeed is typically less than 150 cm/s (e.g., peak commoncarotid artery blood flow speed is approximately 66 cm/s [26]).The two algorithms showed well-matched pairing results thatwere over 80% for blood flow speed limit greater than 75 cm/s,about 90% for the 50 cm/s limit used in this paper, and nearly100% for speed limit less than 25 cm/s, which is also thepoint when the pairing distance curves of the two algorithmseventually merged.

There are some limitations of this paper. First, the proposedmethods were tested on an in vivo rabbit kidney data set wherethe ground truth of the microvessel structure and microvesselblood flow speed was unknown. The microvessel structure canbe potentially validated with other imaging techniques such asmicro-computed tomography. However, the microvessel bloodflow speed may be difficult to validate in vivo. A simulationplatform or a tissue mimicking microflow phantom with appro-priate in vivo microvessel hemodynamics and noise charac-teristics may be needed for the validation. Second, we didnot compare the proposed tracking methods with existingmicrobubble tracking methods such as the Markov chain-basedtechnique proposed in [2]. This study was designed to show thestep-by-step improvements from the proposed methods basedon the same reference data. Future studies will be conductedto further validate the proposed methods with the existenceof ground truth as well as comparing with other microbubbletracking techniques. And finally, the data set used in this paperwas obtained from a short acquisition that only lasted 5 s,which may result in an insufficient number of microbubbleevents to accurately depict the kidney microvasculature. Witha long-term goal of clinical translation of the super-resolutionimaging technique, in this paper, we performed freehandscanning and allowed the rabbit to breathe freely to bestmimic in vivo human scanning. Also we acquired microbubbledata from only 1 bolus injection (with dose adjusted to theweight of the rabbit), which was also attempting to simu-late a human imaging setup. Combining all these factors,it was challenging to obtain a long and rich microbubbledata set without significant tissue motion that is similar to the150-s data set with 18 bolus injections and fixed transducerscanning used in [1]. At present, the longest robust data set wewere able to acquire lasted 15 s with a total of 4125 frames(as compared to the 5-s data with 1000 frames used above)and ∼3 × 105 microbubble events (single bolus injection).The microvessel perfusion image from this data set is shownin Fig. 19. One can clearly see the significantly improveddetails of the kidney cortical microvessels with this dataset. Future investigations need to be conducted to increasemicrobubble blinking events with a limited dose of bolus injec-tion in clinic and improve the robustness of image registrationto maximize the available microbubble signals that can be usedfor super-resolution imaging of the tissue microvasculature.

V. CONCLUSION

In this paper, we demonstrated significant improvement ofmicrovessel super-resolution imaging by using a spatiotem-poral NLM denoising filter and the bipartite graph-based

microbubble pairing and tracking. The NLM filter effectivelyrejected ultrasound noise and preserved the microbubble signalwithout significant blurring, facilitating more robust microbub-ble localization. The bipartite graph-based pairing with persis-tence control further suppresses unreliable microbubble signalsand enhances the microvessel imaging quality as well as theconsistency of microvessel blood flow speed measurement.This study demonstrated visualization of microvessels as smallas 57 μm and separation of microvessels that are 76 μmapart at 2-cm depth from a freely breathing rabbit witha freehand ultrasound scan, paving the way for the futureclinical translation of the microvessel super-resolution imagingtechnique.

REFERENCES

[1] C. Errico et al., “Ultrafast ultrasound localization microscopy for deepsuper-resolution vascular imaging,” Nature, vol. 527, pp. 499–502,Nov. 2015.

[2] D. Ackermann and G. Schmitz, “Detection and tracking of multiplemicrobubbles in ultrasound B-mode images,” IEEE Trans. Ultrason.,Ferroelect., Freq. Control, vol. 63, no. 1, pp. 72–82, Jan. 2016.

[3] K. Christensen-Jeffries, R. J. Browning, M.-X. Tang, C. Dunsby, andR. J. Eckersley, “In vivo acoustic super-resolution and super-resolvedvelocity mapping using microbubbles,” IEEE Trans. Med. Imag., vol. 34,no. 2, pp. 433–440, Feb. 2015.

[4] O. M. Viessmann, R. J. Eckersley, K. Christensen-Jeffries,M. X. Tang, and C. Dunsby, “Acoustic super-resolution with ultrasoundand microbubbles,” Phys. Med. Biol., vol. 58, no. 18, pp. 6447–6458,Sep. 2013.

[5] F. Lin, S. E. Shelton, D. Espíndola, J. D. Rojas, G. Pinton, andP. A. Dayton, “3-D ultrasound localization microscopy for identifyingmicrovascular morphology features of tumor angiogenesis at a resolutionbeyond the diffraction limit of conventional ultrasound,” Theranostics,vol. 7, no. 1, pp. 196–204, 2017.

[6] A. Bar-Zion, C. Tremblay-Darveau, O. Solomon, D. Adam, andY. C. Eldar. (2016). “Fast vascular ultrasound imaging with enhancedspatial resolution and background rejection.” [Online]. Available:ht.tps://arxiv.org/abs/1601.05710

[7] K. B. Hansen et al., “Robust microbubble tracking for super resolutionimaging in ultrasound,” in Proc. IEEE Int. Ultrason. Symp. (IUS),Sep. 2016, pp. 1–4.

[8] O. Couture, B. Besson, G. Montaldo, M. Fink, and M. Tanter,“Microbubble ultrasound super-localization imaging (MUSLI),” in Proc.IEEE Int. Ultrason. Symp., Oct. 2011, pp. 1285–1287.

[9] Y. Desailly, J. Pierre, O. Couture, and M. Tanter, “Resolution limits ofultrafast ultrasound localization microscopy,” Phys. Med. Biol., vol. 60,no. 22, pp. 8723–8740, Nov. 2015.

[10] C. F. Dietrich, M. A. Averkiou, J. M. Correas, N. Lassau, E. Leen,and F. Piscaglia, “An EFSUMB introduction into dynamic contrast-enhanced ultrasound (DCE-US) for quantification of tumour perfusion,”Ultraschall Med., vol. 33, no. 4, pp. 344–351, Aug. 2012.

[11] G. Montaldo, M. Tanter, J. Bercoff, N. Benech, and M. Fink, “Coherentplane-wave compounding for very high frame rate ultrasonography andtransient elastography,” IEEE Trans. Ultrason., Ferroelect., Freq. Con-trol, vol. 56, no. 3, pp. 489–506, Mar. 2009.

[12] P. Coupe, P. Hellier, C. Kervrann, and C. Barillot, “Nonlocal means-based speckle filtering for ultrasound images,” IEEE Trans. ImageProcess., vol. 18, no. 10, pp. 2221–2229, Oct. 2009.

[13] S. Jonas, D. Bhattacharya, M. K. Khokha, and M. A. Choma, “Microflu-idic characterization of cilia-driven fluid flow using optical coherencetomography-based particle tracking velocimetry,” Biomed. Opt. Exp.,vol. 2, no. 7, pp. 2022–2034, 2011.

[14] M. D. Plummer and L. Lovász, Matching Theory. Amsterdam,The Netherlands: Elsevier, 1986.

[15] A. Buades, B. Coll, and J.-M. Morel, “A review of image denoisingalgorithms, with a new one,” Multisc. Model. Simul., vol. 4, no. 2,pp. 490–530, 2005.

[16] H. W. Kuhn, “The Hungarian method for the assignment problem,”Naval Res. Logistics Quart., vol. 2, nos. 1–2, pp. 83–97, Mar. 1955.

[17] J. Munkres, “Algorithms for the assignment and transportation prob-lems,” J. Soc. Ind. Appl. Math., vol. 5, no. 1, pp. 32–38, 1957.


[18] Y. Cao. (2008). Munkres’ Assignment Algorithm. [Online]. Available:ht.tp://csclab.murraystate.edu/~bob.pilgrim/445/munkres.html

[19] V. Hingot, C. Errico, M. Tanter, and O. Couture, “Subwavelengthmotion-correction for ultrafast ultrasound localization microscopy,”Ultrasonics, vol. 77, pp. 17–21, May 2017.

[20] W. F. Walker and G. E. Trahey, “A fundamental limit on delay estima-tion using partially correlated speckle signals,” IEEE Trans. Ultrason.,Ferroelect., Freq. Control, vol. 42, no. 2, pp. 301–308, Mar. 1995.

[21] C. Demené et al., “Spatiotemporal clutter filtering of ultrafast ultrasounddata highly increases Doppler and fultrasound sensitivity,” IEEE Trans.Med. Imag., vol. 34, no. 11, pp. 2271–2285, Nov. 2015.

[22] P. Song, A. Manduca, J. D. Trzasko, and S. Chen, “Ultrasound smallvessel imaging with block-wise adaptive local clutter filtering,” IEEETrans. Med. Imag., vol. 36, no. 1, pp. 251–262, Jan. 2017.

[23] C. Errico, B.-F. Osmanski, S. Pezet, O. Couture, Z. Lenkei, andM. Tanter, “Transcranial functional ultrasound imaging of the brain usingmicrobubble-enhanced ultrasensitive Doppler,” NeuroImage, vol. 124,pp. 752–761, Jan. 2016.

[24] D. B. West, Introduction to Graph Theory, vol. 2. Upper Saddle River,NJ, USA: Prentice-Hall, 2001.

[25] S. Suri. (2006). Bipartite Matching & the Hungarian Method. [Online].Available: ht.tp://www.cs.ucsb.edu/~suri

[26] R. E. N. Shehada, R. S. C. Cobbold, K. W. Johnston, and R. Aarnink,“Three-dimensional display of calculated velocity profiles for physiolog-ical flow waveforms,” J. Vascular Surgery, vol. 17, no. 4, pp. 656–660,Apr. 1993.

Pengfei Song (S’09–M’14) was born in Weihai,China, in 1986. He received the B.Eng. degree inbiomedical engineering from the Huazhong Uni-versity of Science and Technology, Wuhan, China,in 2008, the M.S. degree in biological systems engi-neering from the University of Nebraska–Lincoln,Lincoln, NE, USA, in 2010, and the Ph.D. degreein biomedical sciences-biomedical engineering fromMayo Graduate School, Mayo Clinic College ofMedicine, Rochester, MN, USA, in 2014.

He is currently an Assistant Professor with theDepartment of Radiology, Mayo Clinic College of Medicine. His currentresearch interests include ultrasound microvessel imaging and ultrasound shearwave elastography.

Dr. Song is a member of AIUM and Sigma Xi.

Joshua D. Trzasko (M’99–SM’14) received the B.S.degree in electrical and computer engineering fromCornell University, Ithaca, NY, USA, in 2003, andthe Ph.D. degree in biomedical engineering fromMayo Graduate School, Mayo Clinic College ofMedicine, Rochester, MN, USA, in 2009.

He is currently an Assistant Professor of radiol-ogy and biomedical engineering with Mayo Clinic,Rochester, MN, USA. His research focuses on thedevelopment and application of statistical signalprocessing methods for medical imaging, including

quantitative imaging, artifact correction, and limited data reconstruction inmagnetic resonance imaging, radiation dose reduction in X-ray computedtomography, and ultrasound microvasculature imaging.

Armando Manduca (M’89) received the B.S.degree in mathematics from the University of Con-necticut, Storrs, CT, USA, in 1974, and the Ph.D.degree in astronomy from the University of Mary-land, College Park, MD, USA, in 1980.

He is currently a Professor of biomedical engi-neering, a Professor of radiology, and Chair of theDivision of Biomathematics and Translational Engi-neering, Mayo Clinic, Rochester, MN, USA. Hiscurrent research interests include the developmentof algorithms for the analysis of magnetic resonance

and ultrasound elastography data, image denoising for computed tomographydata to reduce radiation dose, and ultrasound microvessel imaging.

Runqing Huang received the Ph.D. degree inimaging and nuclear medicine from Tongji MedicalSchool, Huazhong University of Science and Tech-nology, Wuhan, China, in 2004.

She is currently a Principal Research Technologistwith the Division of Cardiovascular Diseases, MayoClinic, Rochester, MN, USA. Her research focuseson the diagnostic applications of contrast-enhancedultrasound imaging.

Ramanathan Kadirvel received the M.Sc. degreein biochemistry from Bharathidasan University,Tiruchirappalli, India, in 1998, and the Ph.D. degreein biochemistry from the University of Madras,Chennai, India, in 2002.

He joined Mayo Clinic, Rochester, MN, USA,in 2003, where he is currently an Associate Professorof radiology. His research focuses on understandingthe healing mechanisms of intracranial aneurysmsfollowing endovascular treatments.

David F. Kallmes received the B.S. degree inchemical engineering from the Virginia PolytechnicInstitute and State University, Blacksburg, VA,USA, and the medical degree from the Universityof Massachusetts Medical School, Worcester,MA, USA.

His residency was carried out at DukeUniversity, Durham, NC, USA, and thereafterhe completed his Diagnostic and InterventionalNeuroradiology Fellowship at the University ofVirginia, Charlottesville, VA, USA. He is currently

an Interventional Neuroradiologist with Mayo Clinic, Rochester, MN,USA. He has been focused on the diagnosis and treatment of saccular andintracranial aneurysms.

Shigao Chen (M’02–SM’15) received the B.S.and M.S. degrees in biomedical engineering fromTsinghua University, Beijing, China, in 1995and 1997, respectively, and the Ph.D. degree in bio-medical imaging from the Mayo Graduate School,Mayo Clinic College of Medicine, Rochester, MN,USA, in 2002.

He is currently an Associate Professor with theMayo Clinic College of Medicine. His researchinterests include the noninvasive quantification ofthe viscoelastic properties of soft tissue using ultra-

sound, and ultrasound microvessel imaging.

Documents

IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND … · 2018. 8. 29. · 150 IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, VOL. 65, NO. 2, FEBRUARY