IOP PUBLISHING LASER PHYSICS LETTERS

Laser Phys. Lett. 10 (2013) 035603 (5pp) doi:10.1088/1612-2011/10/3/035603

LETTER

Application of RPCA in optical coherencetomography for speckle noise reduction

F Luan1 and Y Wu2

1 College of Information Science and Engineering, Northeastern University, Shenyang, 110819,People’s Republic of China2 School of Materials and Metallurgy, Northeastern University, Shenyang, 110819,People’s Republic of China

E-mail: luanfeng1979@hotmail.com

Received 27 March 2012Accepted for publication 4 December 2012Published 24 January 2013Online at stacks.iop.org/LPL/10/035603

AbstractOptical coherence tomography (OCT) is a promising technology, which could be used in avariety of imaging applications. However, OCT images are usually degraded by speckle noise.Speckle noise reduction in OCT is particularly challenging because it is difficult to separatethe noise and the information components in the speckle pattern. In this study, a novel specklenoise reduction technique, based on robust principal component analysis (RPCA), is presentedand applied to OCT images for the first time. The proposed technique gives an optimalestimate of OCT image domain transformations such that the matrix of transformed OCTimages can be decomposed as the sum of a sparse matrix of speckle noise and a low-rankmatrix of the denoised image. The decomposition is a unique feature of the proposed methodwhich can not only reduce the speckle noise, but also preserve the structural information aboutthe imaged object. Applying the proposed technique to a number of OCT images showedsignificant improvement of image quality.

(Some figures may appear in colour only in the online journal)

1. Introduction

Optical coherence tomography (OCT) is a modern biomedicalimaging technology based on low coherence interferometry(LCI). OCT allows for non-contact, high-resolution imagingof biological tissues [1]. Over the past 20 years, OCT’sdevelopment has been remarkable. With rapid progress, OCTis now often cited as a promising tool, which could beused in a variety of imaging applications. Since OCT isbased on detection of coherent waves, OCT images containspeckle. Speckle in OCT is dependent on the wavelength ofthe imaging beam and the structural details of the imagedobject [2]. Time varying speckle in OCT structural imagescan be used in the analysis of tissue structure and flowinformation [3–5]. In [6] it is mentioned that the specklecontent present in depth OCT images can be utilized to

differentiate various tissue types, such as skin, lung, fatand breast tissue. The speckle variance OCT method canalso be used to delineate tissue micro vasculature in vivoaccording to its different temporal speckle decorrelationcharacteristics [7, 8]. Speckle variance imaging provides amore accurate representation of the vascular structure [9].As mentioned above, we believe that there are informationcomponents representative of the imaged object in thespeckle pattern. Unfortunately, speckle also carries a noisecomponent, which is responsible for the grainy appearanceof OCT images [10–12]. Reduction of speckle noise canincrease the image contrast and spatial resolution, thereforeallowing further visualization of the imaged object [13].However, speckle noise reduction in OCT is particularlychallenging because it is difficult to separate the noise and theinformation components in the speckle pattern [10–12]. Much

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Laser Phys. Lett. 10 (2013) 035603 F Luan and Y Wu

research has been performed over the years on OCT specklenoise reduction. The results presented in [13] demonstratethat speckle noise can be reduced by using optical clearingosmotic agents, however this kind of technique requiresmodifications to the OCT system design. Therefore, thedevelopment of post-processing techniques for speckle noiseattenuation is preferable to design modification, and it isan important part of the OCT imaging [10, 14]. In orderto reduce speckle noise, two-dimensional OCT images areaveraged in the lateral direction into a single curve [15–19].In some research, an averaging technique is employed forspeckle noise suppression [20–23], however it results ina one-dimensional curve that impedes further performance,such as image segmentation and pattern recognition. Wavelettransforms have also been applied in the OCT images forspeckle noise reduction and obscured pattern recognition [35,36] as well as other applications in the fields of laserphysics [24–34]. For example, [36] indicates wavelet analysiscan enhance the OCT imaging capabilities and reduce thestatistical noise associated with multiple scattering.

Principal component analysis (PCA) has been widelyused for data processing, analysis and dimensionalityreduction in the fields of laser physics. For example,in order to derive knowledge of the reference spectradatabase, the PCA approach is applied to determine individualautofluorescence components [37]. The PCA method is usedto identify different isolates for the detection of biofilm-positive and biofilm-negative staphylococcus epidermidisstrains [38]. In a different study, PCA is employed to identifymalignant tissue/cells and classify the data, and the resultsare indicated to be effective for the Raman spectral diagnosisof oral mucosal diseases [39]. However, many researchworks in the literature have proposed ways of addressingthe limitations of classical PCA with respect to outliers andgross corruption over recent decades, yielding the field ofrobust PCA (RPCA) [40–44]. In this paper, a novel specklenoise reduction technique, based on the RPCA technique, ispresented and applied to OCT images for the first time. Theproposed technique gives an optimal estimate of OCT imagedomain transformations such that the matrix of transformedOCT images can be decomposed as the sum of a sparse matrixof speckle noise and a low-rank matrix of the denoised image.We verified the efficacy of the proposed technique with anumber of experiments on both posterior and anterior eyeOCT images.

2. Materials and methods

In OCT, the observed image is a superposition of theinformation component and the noise component in thespeckle pattern, therefore, the component of the OCTimage has low intrinsic dimensionality, i.e., it lies in somelow-dimensional subspace, or it is sparse. Mathematically, thismeans the observed OCT image X can be decomposed into alow-rank matrix and a sparse matrix such that X = XL + XS,where XL has low rank and XS is sparse. Obviously, thecomponent XL carries the information of the imaged object,and the component XS carries the speckle noise. Given these

Figure 1. Original posterior eye OCT image with ROIs overlaid inwhite. Region 1 was used to calculate the background noise level. Atotal of three inhomogeneous regions (2, 3 and 4) along with threehomogeneous regions (5, 6 and 7) were considered.

properties of RPCA, we present in this work a novel approachbased on RPCA to reduce speckle noise in OCT images.Our results indicate that the image quality is significantlyimproved. The proposed approach is defined as the followingconstrained minimization of a cost function,

minXL,XS

‖XL‖∗ + γ ‖XS‖1 subject to X = XL + XS (1)

where ‖ · ‖∗ denotes the matrix nuclear norm, ‖ · ‖1 denotesthe L1 norm, and γ is a positive weighting parameter tobalance the two terms, with γ = 1/

√max(D,T), where D is

the number of axial pixels of the observed OCT image, and Tis the number of transverse pixels of the OCT image. For theOCT imaging problem, we do not know the low-dimensionalsubspace of XL or the locations and number of the nonzeroentries of XS. There are several algorithms for solving theRPCA problem [40–44]. In this work, we adopt a fast andaccurate algorithm for the low rank and sparse decompositionof OCT images, namely the inexact augmented Lagrangemultiplier (IALM) method [40].

The approach was tested on the retinal image ofophthalmic OCT. The Copernicus SD OCT HR (OptopolTechnology S.A., Zawiercie, Poland) instrument was usedto collect the OCT data. The details of the OCT imageinformation have been previously described in [45]. Toquantify the performance of the proposed method, well-known speckle noise reduction performance metrics suchas peak-signal-to-noise ratio (SNR), contrast-to-noise ratio(CNR), equivalent number of looks (ENL), and crosscorrelation (XCOR) were computed. CNR measures thecontrast between image features and noise. ENL measuresthe smoothness of areas that should have a homogeneousappearance but are corrupted by speckle noise. XCOR

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Laser Phys. Lett. 10 (2013) 035603 F Luan and Y Wu

Figure 2. (a) Original OCT image. (b) Denoising result of RPCA.

Figure 3. The cross section signal along the white solid line in (b). ILM/NFL, inner limiting membrane/nerve fibre layer; IPL, innerplexiform layer; INL, inner nuclear layer; OPL, outer plexiform layer; ELM, external limiting membrane; IS/OS junction between the innerand outer segment of the photoreceptors; RPE, retinal pigment epithelium; CH/SC junction between the choroid and sclera.

measures the similarity between the images before and afterdenoising. The image quality metrics used are the same as themetrics described in [10–12, 14, 35, 45, 46].

3. Results and discussion

The proposed method was first applied to the posterior eyeOCT image. Figure 1 shows the original image with sixregions of interest (ROIs) overlaid in white. The unprocessed

OCT image has a grainy appearance because of the presenceof speckle. Three inhomogeneous ROIs (labelled 2, 3 and4), three homogeneous ROIs (labelled 5, 6 and 7), and abackground region (labelled 1, for the retinal image it is thevitreous-humour area) were manually selected and marked onthe image.

As shown in figure 2, much of the speckle noise inthe original image has been suppressed by using RPCA,making some image features hidden in the original image

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Laser Phys. Lett. 10 (2013) 035603 F Luan and Y Wu

Figure 4. (a) Original anterior eye OCT image with ROIs overlaid in white. Region 1 was used to calculate the background noise level. Atotal of three inhomogeneous regions (2, 3 and 4) along with three homogeneous regions (5, 6 and 7) were considered. (b) Denoising resultof RPCA.

more obvious. A zoomed region was added in the images inorder to illustrate the speckle reduction and any potential lossof spatial resolution. The RPCA improves the visualizationof small morphological features such as the junction betweenthe inner and outer segment of the photoreceptors (IS/OS) andretinal pigment epithelium (RPE), as indicated in the zoomedregions. Quantitative comparison of the denoising effectfor the RPCA-based method was performed by evaluatingthe image quality metric values for the original and thedenoised images. The results from the quantitative analysisare presented in the lower left corner of figures 2(a) and (b).The CNR values are averaged over six ROIs (2–7). The ENLvalues are averaged over the three homogeneous ROIs (5–7).The first ROI is used to calculate the background noise level.The application of the proposed method resulted in significantperformance improvements over the original image, with anENL improvement of 25.1692 compared to the original image.Moreover, CNR and SNR improvements are also observed.The CNR improves by 0.9643 and the SNR improves by2.9775 with a similarity (XCOR) degradation of only 1.63%.The results demonstrated the effectiveness of the proposedapproach for speckle noise reduction. Although the XCORof the RPCA technique is slightly lower than the originalone, the reduction in speckle noise with the RPCA allows thelayered structure in the image to be more clearly delineatedwhen looking at a cross section signal. Figure 3 presents aone-dimensional cross section of the denoised image at theindicated white solid line in figure 1(b). Figure 3 indicatesthat, after RPCA denoising, both the layer/edge separation ofthe retina and the image features of the original signal are wellpreserved. All of those demonstrated the ability of the RPCAin reducing noise while preserving signals.

The RPCA method was also applied to the OCTimage of an anterior eye with a contact lens. Significantsmoothness enhancement can be clearly seen in figure 4(b)when compared with figure 4(a). The denoised image is muchcleaner than the original one, and the features of the objectare more obvious with the proposed technique. It is worthnoting that the RPCA also increased the CNR, ENL and SNR.The CNR, ENL and SNR were improved by 0.5227, 4.4226

and 2.7532, respectively, while image similarity was degradedby only 3.52%. These results suggest that the improvementof image quality was obtained again by using the RPCAtechnique.

4. Conclusion

In this study, we demonstrated the efficacy of a RPCA-basedtechnique to reduce speckle noise in OCT images. Thedecomposition of the OCT image matrix into a sparse matrixof speckle noise and a low-rank matrix of denoised imageis a unique feature of the proposed method which cannot only reduce the speckle noise, but also preserve thestructural information about the imaged object. In general,the application of this technique to the post-processing ofOCT images significantly improved the image quality. Theresults suggest that RPCA-based speckle noise reductioncould be a powerful technique for many future OCT imagingapplications.

Acknowledgment

This work was supported in part by the National NaturalScience Foundation of China (grant no. 61201054).

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