I. PARTICIPANTS II. PROJECT DESCRIPTION

I. PARTICIPANTS

II. PROJECT DESCRIPTION

A. Project Overview

The development of energy-selective photon counting detectors for X-ray sensing applications has created the possibility to significantly enhance materials characterization capabilities, relative to existing energy-integrating or dual-energy systems. Energy-integrating methods provide information only regarding material density, while dual-energy systems, at best, can image both density and effective atomic number (or equivalently spatial maps of Compton and photoelectric coefficients). In practice, the overlapping nature of the spectra employed in fielded dual-energy systems, as well as the nature of X-ray physics, significantly complicates the stable recovery of the atomic number and photoelectric coefficient (PE). Multi- or hyper-spectral forms of sensing, where data are collected over a large number of narrow energy bins in such a manner as to reflect both attenuation as well as X-ray scattering, have the potential to move X-ray based screening significantly beyond the limitations of the current state-of-the-art systems.

In more detail, the energy-integrating and dual-energy methods recover information concerning the object of interest based on the way X-rays are attenuated as they pass through the medium. The attenuation properties reflect both the absorption of the X-rays and the scattering of the X-ray photons from the beam. For all of the fielded X-ray systems in use by the Department of Homeland Security (DHS), these scattered photons are typically ignored, but the work in this project has begun to demonstrate that these photons have significant information embedded in them. With appropriate processing, this information can enhance materials characterization from X-ray data, specifically in the context of limited-view systems currently under investigation and development. In recent years, DHS has been exploring X-ray systems comprised of spatially fixed sources and detectors, in contrast to traditional computed tomography (CT) types of systems where the source/detector arrays rotate around the items being scanned. Complicating the development of these systems, the limited number of source/detector paths compared to the full-scale CT case creates substantial challenges in terms of image formation and, ultimately, target detection. Using the detectors in these systems to collect scattered photons (in addition to the traditional attenuation-based data) significantly increases the information content in the data even for these fixed geometries.

In this regard, we consider two scattering process for the energy range of interest in this application domain. The first, Compton scattering, is characterized by two key properties: (i) its intensity is directly proportional

ALERT Phase 2 Year 6 Annual Report

Appendix A: Project Reports Thrust R4: Video Analytics & Signature Analysis

Project R4-B.2

to the electron density near the event; and (ii) it’s inelastic, meaning that the energy of the photons shifts after a scattering event, thereby necessitating the use of energy-resolving detectors to usefully capture and quantify these processes. The shift in energy determines the direction in which photons are scattered. In a sense, this energy-dependent scattering direction very much “encodes” density at a specific location. These two properties have significant systems-level implications for DHS. The second process, Bragg scattering, is coherent (meaning energy is not lost as a result of the interaction) but it’s highly sensitive to the presence of crystalline structures in the region under investigation (i.e. the resulting geometric patterns observed in energy-resolved data where the interactions are the strongest). As such, the observation and appropriate processing of Bragg scattered photons hold much promise for identifying important classes of materials.

Realizing this potential, however, requires that we address several challenges. First, the physical processes and mathematical/computational models associated with these scattering processes are more complex than traditional attenuation imaging. The development of a Compton model during Years 1 and 2, which linked the observed data to the material properties of interest, was necessary to address the subsequent challenge. Second, the use of scattered photons to form images, in addition to traditional attenuation data, became the focus of our effort in Years 3–6. Only after these image formation methods are in place can we quantify the true benefits of these new data (e.g. attainable image resolution, reduction in imaging artifacts, target detection, and false alarm rates). While our efforts have focused largely on the Compton signal in Years 3–5, this past year, in collaboration with scientists at Rapiscan Systems, we have begun an intense exploration of the Bragg data as well.

The immediate significance of this project relative to the larger ALERT program lies in the potential of these models and associated processing methods to improve the accuracy of screening checked baggage and luggage inspected at the checkpoint. The algorithms at the heart of the current collection of Transportation Security Administration (TSA) certified systems are not sufficient for processing the data that will be produced by the next generation of X-ray scanning systems. Even the state-of-the-art model based iterative reconstruction methods are not designed to fully exploit the information provided by multi-/hyper-spectral X-ray data. Neither are they capable of addressing the challenges encountered when considering the severely limited-view nature of the data provided by these fixed source/fixed detector systems. Our proposed approach to explore the utility of scattered X-ray information to materials characterization is intended to address both challenges and, to the best of our knowledge, is the only effort within the ALERT program with this focus.

Finally, we note the steps taken by this team in technology transition. As discussed in last year’s report, the initial promise of combining Compton scatter and traditional attenuation data was confirmed by using simulation data by the Tufts-based PhD research assistant, Ms. Hamideh Rezaee, whose efforts have been directly supported by the ALERT center. Based on her results, the team from Tufts and the scientists from American Science and Engineering (AS&E) were supported under a DHS “13-05” project mid-2016 to mid-2017 to build a testbed system and associated processing methods to demonstrate the utility of combining energy resolved scatter and attenuation data in a limited-view geometry for imaging mass density and PE. Notably, imaging results obtained in 2017 using data from this testbed clearly demonstrated similar benefits as Ms. Rezaee saw in her simulations this year, specifically in terms of density reconstruction. The project concluded before we could explore the recovery of photoelectric spatial maps. The transition of this work, initially seeded by ALERT, is continuing in the form of a collaboration between the Tufts group and Drs. Dan Strellis and Ed Morton from Rapiscan, focusing on combining X-ray diffraction, scatter, and attenuation data in a non-rotating source/detector system.



Project R4-B.2

B. State-of-the-Art and Technical Approach

The work conducted at Tufts over the last year has been focused on the Monte Carlo simulation of the Bragg and Compton scattered signals, with a focus on the Rapiscan RTT (Real Time Tomography) machine geometry developed by our collaborators at Rapiscan. A spatially normalized, two-dimensional model for this system is provided in Figure 1.

Here we have an array of X-ray sources located along the line 𝑧 = 𝑠 = 3, and two arrays of detectors:

1. Typical transmission data (line integrals of attenuation) are collected over rays connecting source points at 𝑧 = 𝑠 to detectors situated along the line 𝑧 = 𝑑𝐴.

2. Inelastically scattered (Compton) data are acquired in a backscatter geometry by detectors located at 𝑧 = 𝑑𝐶 = 1. Here we assume backscatter data are measured only for detectors located at the same (𝑥, 𝑦) coordinates as the corresponding source. For example, in Figure 1, the Compton signal for the source located at (𝑥, 𝑦, 𝑧) = (0,0,3) will be recorded by a detector at (𝑥, 𝑦, 𝑧) = (0,0,1). That signal will be proportional to the integral of electron density over the portion of the two circles (whose union is known as a toric section) lying between 𝑧 = 𝑑𝐶 and 𝑧 = 𝑑𝐴. See [1] for more details. As the source-detector pairs translate along 𝑥, the corresponding circle sections will likewise move. Moreover, as the energy of the transmitted photons increases (resp. decreases), the radii of these circles decreases (resp. increases). Thus, the combination of source-detector spatial diversity and the energy spread associated with typical X-ray sources (such as an X-ray tube [2]) provides a Radon-like collection of partial toric section integrals of electron density covering the region of interest. Finally, we note that the actual RTT system has sources and detectors along four sides of a box geometry. For simplicity, our work to date has focused on the simpler case illustrated in Figure 1.



Project R4-B.2

3. Elastically scattered X-ray photons—whose interaction with crystalline (or polycrystalline) material are governed by the Bragg scattering process [3]—are collected by linear arrays of detectors along the line 𝑧 = 𝑑𝐴 but coming “out of the page” at different 𝑦 coordinates. The 𝑖-th of these detector arrays is columnated to observe Bragg scattered photons along a line 𝑧 = 𝑑𝐵𝑖

with 𝑑𝐴 < 𝑑𝐵𝑖< 𝑑𝐶 .

Because the entire array is sensitive to a collection of parallel lines of Bragg scatter, we refer to this as a “Venetian blind” collimation.

Our Monte Carlo (MC) package simulates particle interactions in a similar vein to the GEANT4 [4] package, on a photon by photon basis with the scattering directions sampled from the Bragg [5] and Compton [6] differential cross sections. The code is written in Matlab, which allows for visualization and ease of use, although at a cost of computational efficiency. We have also developed analytic physical models for the Bragg and Compton signal, based on the theory of [5–8] which has led to the derivation of new reconstruction techniques for the image recovery of the crystal structure and electron density of airport baggage. Our MC code is not specific to the RTT geometry; it can be adapted to simulate the photon counts for a general machine geometry. Hence, we aim to apply our software to advance research in Compton Scattering Tomography (CST) fields. In CST, the theoretical aspects of electron density imaging are well established (particularly in two dimensions), however, the empirical validation of the inversion techniques proposed in the literature is lacking. We aim to tackle this in our work.

The Bragg scatter from a small sample of crystalline powder (i.e. a randomly orientated lattice) is known to appear as a set of rings, as found in experiments such as Debye-Scherrer [9–10] or the left-hand side of Figure 2. Here, we used our MC software to simulate the Bragg patterns from a small sample (a single pixel, size 1 𝑚𝑚3) of Al powder, with an initial photon energy of E=13.8keV.

We consider an RTT-type geometry shown in Figure 3 with an Al point sample located at the origin (O) and β=0. Rather than a collimated set of arrays coming in and out of the page, here we assume a continuous detector plane, which allows us to easily visualize the Debye-Scherrer rings. Knowing the scanning geometry and the position of the sample, we can determine the crystal structure by measuring the radii of the projected rings. This is a classical idea in spectroscopy for determining the crystal structure of powders.



Project R4-B.2

𝜷 𝜷

,

In the desired application in airport baggage screening, we expect to encounter crystalline material in carry-on luggage, and the sample size will likely be far larger than a single pixel (by an order of 𝑐𝑚3 in volume). As noted above, the detector arrays on the RTT machine will be collimated to planes (in a Venetian blind collimation), and the sources are fan beams, where the initial photon output is also constrained to a plane. We can model the scattered intensity at the RTT detector array as the scattering contribution from a line (i.e. the intersection of two planes; namely the source fan plane and the detector collimation plane) of crystalline material. This appears as the union of a set of Bragg rings in the data (i.e. a union of ellipses that are the projections of Bragg cones onto the detector plane). See the right-hand side of Figure 2, where we have simulated the Bragg signal in an idealized setting: with a high source emission time, neglecting attenuation and self-absorption effects, from a line segment of Al at E=13.8keV.

Given the detector collimation used with the RTT, we only have access to the central line profiles of the plane data displayed in Figure 2 (i.e. the sum of rows 180–220 in Figure 2, which are displayed in Figure 4). Here we see a noisy signal with large jump singularities in the data, which occur at the corresponding Bragg angles. (Such angles, θ, are highlighted when the Bragg equation is satisfied for the given incoming photon energy and position of the Al line relative to the detector plane.) If we take the first derivative of the signal approximated by a finite difference—which reverses the blurring due to the finite volume of the crystal, in a sense—then we reduce the data to the form of its characteristic Bragg peaks (as in [9–10]), from which the crystal structure is determined by the Bragg equation. For the example presented here, we were able to successfully determine the crystal structure (namely, face-centered cubic (FCC)) and lattice spacing (4.07 Angstroms) of the Al material. By combining techniques from classical physics and the collimation ideas that allow for a more stable recovery of the crystal structure of Rapiscan, we have begun to lay the foundations for Bragg scattering tomography and spectroscopy in baggage screening applications. In the coming year, we shall continue the development of this method, including special consideration of effects likely to be seen in practice, such as self-attenuation and the resulting low count rates.



Project R4-B.2

The second main venture at Tufts has been the derivation of new explicit inversion formulae and injection results in CST, based on the RTT portal geometry. The CST problem in the RTT geometry lead our research to a new set of integral transforms in 2D and 3D, where the goal was to reconstruct the electron density from sets of toric sections (2D) and apples (3D, see Figure 1 for a definition of apple surfaces) integral data. The set of toric sections (2D problem) considered are those which remain vertical (with axis of reflection parallel to the 𝑧 axis) and are parameterized by the radius variable 𝑟 and a 1D translation in the 𝑥 direction (so in total a 2D dataset). The set of apples (3D problem) considered are those which are vertical (with axis of revolution parallel to the 𝑧 axis) and parameterized by the radius variable 𝑟 and a 2D translation in the (𝑥, 𝑦) plane (so in total a 3D dataset). We successfully solved the theoretical inversion problem, and now we are formulating our results as a research article, which we aim to publish in The Journal of Inverse Problems. This work significantly extends the CST literature and the works of [11–13]. Now that the mathematical foundations are in place for Compton imaging with the RTT, we can also use our MC code to simulate toric integral data in a practical setting. We have already begun the validation of our analytic Compton model (in the case of a point scatterer), and the results match up well with MC data. See Figure 5. Here, the photons are backscattered (i.e. at a scattering angle greater than 90 degrees), and at an energy of E=125keV. We expect the majority of high energy backscatter to be Compton (or incoherent scatter). Referring again to Figure 3, in that experiment, the point Compton scatterer was placed at the origin (O) and the plane orientation was β=π to collect backscattered photons. Conversely, we expect the forward (i.e. scattering angle of less than 90 degrees) low energy scatter to be dominated by the coherent (i.e. Bragg) processes.



Project R4-B.2

A more recent goal of the team at Tufts is the joint reconstruction of the attenuation coefficient (related to transmission data via the Radon transform) and the electron density (related to Compton data via toric section integral data). The idea is to achieve a better edge recovery of both quantities by enforcing a similarity in the image wavefront sets in the reconstruction process. The wavefront set (defined formally in [14]), loosely speaking, describes the set of singularities (edges) of a function (image) and the directions in which they occur. Enforcing a similarity in the image wavefront sets in the inversion therefore aims to better resolve the image edges in all directions in both reconstructions simultaneously. This uses new regularization techniques based on ideas in microlocal analysis and lambda tomography (in particular using the theorems of [15]). Furthermore, the regularized inverse problem we propose is purely linear (much like the Tikhonov regularized inverse problem [16]), and we can readily apply established iterative linear least squares solvers (such as the conjugate gradient least squares (CGLS) algorithm [17]) to obtain our solution.

As an example, consider the image phantoms displayed in Figure 6, which are rectangular and circular objects with relative densities one and two, respectively. When we reconstruct the phantoms separately from the noisy line integral (with a noise level of 10%) and the toric section integral data, we see significant artifacts in the reconstruction even when using a state-of-the-art Total Variation (TV) [19] regularizer. (The noisy line integral determines the attenuation coefficient [18] and the toric section integral data determines the electron density [1].)



Project R4-B.2

See Figure 7. The separate density and attenuation coefficient reconstructions with a TV regularizer are due to the geometric properties of the RTT and limited data. The set of scattering detectors 𝑑𝐶 and transmission detectors 𝑑𝐴 in the 2D RTT geometry are highlighted in Figure 1. The scattering data are the integrals of the electron density over a 2D set of toric sections. The transmission data are the integrals of the attenuation coefficient over the set of lines intersecting the source 𝑧 = 𝑠 and 𝑧 = 𝑑𝐴 line segments. The work in [1] and [18] provide mathematical analyses either rigorously justifying or at least suggesting the connections between the geometry of the artifacts observed in Figure 7 to the two data acquisition geometries. Specifically, we notice that the edges in the vertical direction are well resolved in the density image, whereas the horizontal singularities are blurred out in the image. We see the opposite effect in the attenuation image reconstruction, much like the image reconstruction presented in [18]. When the two datasets are combined, however, and we apply the microlocal regularizers developed by the Tufts group, we see a significant improvement in the image quality of both images.

In Figure 8, we use the complimentary transmission and scattered data in conjunction with new regularization techniques to resolve the edge effects in all directions with a significant noise level. These ideas show promise for improving the image quality in practical Eapplications in baggage screening and introduce a new form of regularization which is of interest in inverse problems fields. We aim to continue to pursue such ideas to address the aims of our collaborators at Rapiscan and in advancing the research outcomes of the Tufts group.



Project R4-B.2

C. Major Contributions

C.1. Year 6

The research advances made over the last year by the Electrical and Computer Engineering group at Tufts are summarized as follows: Ms. Hamideh Rezaee, the Tufts PhD student who has been supported by ALERT for the past four years,

successfully defended her doctoral dissertation and published a paper in the IEEE Transactions on Computational Imaging, on the model-based fusion of attenuation and scatter X-ray data for the joint recovery of electron density and photoelectric absorption.

In support of our growing collaboration with Rapiscan Systems (Drs. Ed Morton and Dan Strellis) we have begun the development of new Monte Carlo (MC) software for the simulation of the transmitted and scattered signals from randomly orientated crystalline lattices (powders) and amorphous materials. This has provided valuable insight for our collaborators at Rapiscan on the expected photon counts and imaging capabilities of a new RTT portal scanner developed by the company.

We have also developed new inversion formulae in Compton Scattering Tomography (CST), based on the RTT geometry. This is a significant advancement on the current literature in CST, and we aim to publish our results in the most relevant inverse problems journal.

We are in the process of developing a new joint reconstruction technique which uses a combination of the transmitted and scattered signal to improve the edge recovery in the joint reconstruction of the attenuation and density images. Initial results of using this method, based on ideas in lambda tomography and microlocal analysis, appear to be effective in the edge recovery of simulated phantoms in 2D, with high levels of added pseudo random noise. One objective over the coming year is to continue the exploration of this method.

C.2. Year 5

In the process of writing a manuscript detailing the processing method developed by our group under support from ALERT, the reviewers of the paper asked us to test the approach on data sets that were more realistic than those employed to date. To meet this need, we have considered: (a) the generation of data with Poisson statistics based on the single scatter model used in the processing (i.e. model matched data); as well as (b) the creation of data using sophisticated MC codes (specifically, GEANT4) which, in essence, contain “all” of the physics that would be seen in experimentally obtained data. We have developed a collaboration with Dr. Peter Rothschild of Heuresis Corporation to generate the MC simulation data for a number of test scenarios. The effort of generating the data and reducing it to a form that can be put into our algorithms has taken most of Fall 2017 and Winter 2018. Between late Winter 2018 through the writing of this report, we have focused on the processing of the Poisson and MC data. Initial results demonstrate that even within the context of severely limited-view geometries, our formulation of the imaging problems clearly demonstrates that the addition of scatter data to the processing provides significant benefits in terms of recovering the density relative to attenuation-only data sets. It is likely that accurate recovery of the photoelectric signature will not be possible in this data acquisition scenario. We hypothesize that sparse angle data (i.e. data acquired from a small number of angles that fully encircles the object) should yield a much improved performance. Moreover, such a data acquisition geometry is consistent with the system to be considered under our upcoming DHS Broad Agency Announcement 17-03 (BAA 17-03) project with Rapiscan Systems. This ALERT project will transition its ideas to vendors from this fundamental component.



Project R4-B.2

C.3. Year 4

The initial image formation method developed in Year 3 was refined due to testing the approach on test cases that were far more complex than those considered during Year 3. In Year 4, we achieved the objectives which were outlined in the Year 3 project report. First, we developed an objective method based on the discrepancy principle for choosing the regularization parameters defining the cost functions used as the basis for estimating both the mass density and photoelectric (PE) images from X-ray observations. Second, we augmented the Compton data with energy resolved attenuation data and demonstrated the gain achieved from the fusion of these two data types. Finally, building on our prior efforts in multi-energy CT, we developed a method for stabilizing the recovery of the PE image, which is based on the use of a NLM (non-local means) regularization scheme.

C.4. Year 3

We have demonstrated a method for joint recovery of both density as well as the photoelectric coefficient from severely limited-view, multi-energy Compton scatter data. The overall approach is based on a variational formulation of the imaging problem. Physical intuition has guided the specific method used to solve this problem. Initial results on simulated data were quite promising.

C.5. Year 2

At the start of Year 2, we decided to move away from the absorption-only model from Year 1 as we began to explore the potential for scattered photon data to address the many challenges associated with the processing of limited-view information. We developed a tractable, analytical model capable for X-ray scattering and attenuation. The model was instantiated in the form of a MATLAB-based code that will be made accessible to the broader DHS community. We believe that the model can be used effectively and efficiently in the context of image reconstruction methods seeking to recover spatial maps of electron density and photo-electric absorption information from limited-view, multi-energy X-ray data.

C.6. Year 1

Our initial efforts under Phase 2 of ALERT support was the development of a computational forward model for multi-energy, limited-view X-ray scanner modeled on the AS&E CANSCAN system, the limited-view system that formed the basis for the 13-05 project.

D. Milestones

D.1. Year 6

We completed the work with the MC simulation data to validate the performance of the current image formation methods. Included in this effort was the consideration of sparse angle data acquisition geometries under which we believe the photoelectric maps can be better recovered.

Conclude the project with the development and validation of an alternate image formation approach, rather than the exploration of the system design topic as explained in the Year 5 Work Plan. Based on an initial investigation by Ms. Hamideh Rezaee, we believe that a fruitful course of action is to consider an alternate means of image formation for materials characterization. Instead of mapping photoelectricity and density, the unknowns would be density (a function of space) and attenuation (a function of space and energy). While it is true that attenuation is known to be dependent on mass density, Ms. Rezaee’s initial efforts suggest that making density and attenuation the “primary”



Project R4-B.2

variables will result in a better posed inverse problem than using density and photoelectric absorption. This effort was not completed in Year 6. Rather, in an effort to engage with Rapiscan in the transition of the ideas from Tufts, we chose to pursue the efforts discussed in Section B above as these were of direct relevance to our industrial collaborators. These alternative imaging ideas are of interest as one component of the work between Tufts and Rapiscan in Year 7.

The Tufts and Rapiscan collaboration on the DHS Stationary Gantry CT-XRD project will focus on the simulation and modeling of the X-ray diffraction (coherent X-ray scatter) signature for the small-bore CT-XRD system as well as the development of methods for robustly fusing transmission, Compton scatter, and Bragg scatter data into a coherent and accurate map of material.

D.2. Year 7

Given the close collaboration with Rapiscan in the development of our Year 7 work plan, as well as the success we have had to date in exploring issues of relevance to them, we do not anticipate any substantial programmatic risk.

E. Future Plans/Project Completion (Year 7)

Given the success of our work described in Section B, we aim to extend our ideas to three dimensions, with a focus on the portal scanner geometry. So far, our work on the Compton reconstruction problem in 3D suggests that the problem is uniquely solvable but severely ill-posed. Based on this analysis, we shall build on problems of this class [20–26] in our ALERT and DHS supported work in model-based iterative reconstruction methods. Additionally, we shall build on our prior effort in the development of microlocal filtering methods [1, 27–28] to develop data processing methods that combat the ill-posedness in 3D Compton tomography. We aim to achieve a commercially useful image of charge density for purposes of threat detection.

Our main goals are summarized as follows:

1. To simulate the transmission and scattered data using MC to aid the design of the portal scanner under development by Rapiscan. For example, we will advise on the detector collimation type, the conveyor belt speed, the source voltage and firing patterns, and the machine dimensions (e.g. portal window size, source-detector ring offset, and position).

2. To develop new Bragg tomography and threat classification techniques, combining the established physical models in Bragg scattering with machine learning methods in classification (e.g. neural network architectures).

3. To continue our work on artifact characterization and reduction in microlocal analysis and Compton tomography.

This effort is designed to provide a transition pathway for the physical models and processing methods developed by the Tufts group to be incorporated into existing DHS programs at Rapiscan. The specific technical tasks arise from—and are intended to support—the current DHS-funded BAA 17-03 effort at Rapiscan. This effort builds on an existing partnership between Tufts and Rapiscan in which an ALERT-funded post-doctoral researcher, Dr. James Webber, has been supported to begin exploring some of these RTT-related modeling and image formation issues during the second half of Year 6. In Year 7, we plan on continuing to employ Dr. Webber. To guarantee transition, the Tufts and Rapiscan team will meet once every two weeks via teleconference. These meetings will review progress made in addressing any challenges discussed in previous meetings, identification of new areas of concern, and the development of a plan to address these issues over the coming two-week period. In addition, funds provided to Tufts in prior years by



Project R4-B.2

AS&E and Rapiscan as part of their membership to ALERT will be used to support two trips by Dr. Webber and Professor Miller to Rapiscan Labs in Fremont, CA for multi-day, face-to-face collaborative meetings. Successful completion of this project on June 30, 2020 will take the form of the analyses we perform and the processing methods and models we develop being incorporated directly into the Rapiscan RTT development and deployment effort.

III. RELEVANCE AND TRANSITION

A. Relevance of Research to the DHS Enterprise

The value of this research to the Homeland Security Enterprise (HSE) lies in the potential of these models and processing methods to improve the accuracy of screening checked baggage, as well as luggage inspected at the checkpoint. The algorithms at the heart of the current collection of TSA certified systems are not sufficient for the processing of the data that will be produced by the next generation of X-ray scanning systems. Even state-of-the-art model-based iterative reconstruction methods are not designed to fully exploit the information provided by multi- and hyper-spectral X-ray data. Neither are they immediately capable of addressing the challenges encountered when considering the severely limited-view nature of the data provided by these fixed source/fixed detector systems. Our approach to explore the utility of scattered X-ray information to materials characterization is intended to address both challenges, and to the best of our knowledge, is the only effort within the ALERT program with this focus.

We are seeking to address challenges associated with automated scanning and threat detection in both checked luggage and baggage that is inspected at checkpoints. The overall goal is to determine spatial maps of material properties in an automated manner from multi-energy X-ray data collected in limited-view types of geometries characteristic of many systems currently under development by DHS contractors. Any metric that quantifies the accuracy of the material maps can be used to evaluate the performance of our work including:

Confusion matrices capturing the percentage of correctly and incorrectly labeled pixels for scenarios where ground truth is known.

If one is concerned with purely binary problems (threat object versus all other types of materials), then the receiver operating characteristic, plotting detection probabilities versus false alarm rates, could be developed.

Finally, we could visualize accuracy using uncertainty cloud analysis developed as part of ALERT Task Order 3 and employed in “Tracey, Brian H., and Eric L. Miller. ‘Stabilizing dual-energy X-ray computed tomography reconstructions using patch-based regularization.’ Inverse Problems, Vol. 3, No. 10, 2015: 105004.” These clouds would plot the average value and first standard deviation ellipse of the distribution of photoelectric and electron density over known target regions in our reconstructions. In comparing multiple candidate processing methods, smaller ellipses and means closer to ground truth are indicators of higher accuracy.

B. Potential for Transition

Transition has been affected through our previous collaboration with AS&E and continued collaboration with Rapiscan. The former was a joint DHS BAA 13-05 project led by American Science and Engineering (AS&E) with Tufts University as a subcontract in which AS&E constructed a scanner that was capable of collecting the type of data required by the processing methods being pursued in this ALERT project. Over the 2016-2017 lifetime of that project, the models and processing methods developed with ALERT support were



Project R4-B.2

transferred directly from the graduate student funded by ALERT to the post-doctoral researcher supported by the DHS BAA 13-05, and ultimately, to AS&E itself. In that time, we consistently met the milestones for the project. The first project concerned the development, validation, and transition of numerical models and image formation algorithms for materials mapping using advanced X-ray tomographic processing methods. This work supported both by ALERT as well as DHS (under Contract HSHQDC-15-C-B0012) was a joint effort between Tufts and AS&E, awarded in response to a proposal to the DHS BAA 13-05. Our Year 7 effort will result in continued transition of the models and processing methods from Tufts to Rapiscan Systems (now an affiliate of AS&E), in support of their continued development of Real Time Tomography (RTT) technology through their DHS S&T BAA 17-03 award on Stationary Gantry CT with In-line X-ray Diffraction.

C. Transition Pathway

Please see Section III.B. above.

D. Customer Connections

At AS&E: Drs. Aaron Couture and Jeffrey Schubert. Until the end of the BAA 13-05 project, we met weekly. Since then, we have met once or twice with Dr. Couture who served on the thesis committee of Ms. Hamideh Rezaee, the student being supported by DHS on this ALRERT project.

At Rapiscan: Drs. Dan Strellis and Ed Morton. We meet with both Drs. Strellis and Morton once every two weeks to review progress on our project and plan for future efforts.

IV. PROJECT ACCOMPLISHMENTS AND DOCUMENTATION

A. Peer Reviewed Journal Articles

Pending-

1. Rezaee, H., Rothschild, P., Tracey, B., and Miller, E. L. “On the Fusion of Energy Resolved Scatter and Attenuation Data for Limited-view X-ray Materials Characterization with Application to Security Screening,” IEEE Transactions on Computational Imaging.

B. Student Theses or Dissertations Produced from This Project

1. Rezaee, H. “Fusion of Energy Resolved Scatter and Attenuation Data for Limited-view X-ray Tomography.” Dept. of ECE Tufts University, May 2019.

V. REFERENCES

[1] J. Webber and E. Quinto, “Microlocal Analysis of a Compton Tomography Problem,” arXiv preprint arXiv: 1902.09623, 2019.

[2] R. Behling, Modern Diagnostic X-ray sources: Technology, Manufacturing, Reliability, 2015.

[3] B. Warren, X-ray Diffraction, 1990.

[4] S. Agostinelli et al., “GEANT4-a Simulation Toolkit,” Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors, and Associated Equip, vol. 506, no. 3, pp. 250–303, 2003.



Project R4-B.2

[5] J. J. DeMarco and P. Suortti, “Effect of Scattering on the Attenuation of X Rays,” Physical Review B, vol. 4, no. 4, p. 1028, 1971.

[6] O. Klein and Y. Nishina, “Über die Streuung von Strahlung durch freie Elektronen nach der neuen relativistischen Quantendynamik von Dirac,” Zeitschrift für Physik, vol. 52, no. 11–12, pp. 853–868, 1929.

[7] A. Wilson and V. Geist, “International Tables for Crystallography. Volume C: Mathematical, Physical and Chemical Tables,” Kluwer Academic Publishers, Dordrecht/Boston/London 1992 (published for the International Union of Crystallography), 883 Seiten, ISBN 0‐792‐3‐16‐38X,” Cryst Res Technol, vol. 28, no. 1, pp. 110–110, 1993.

[8] J. Hubbell and I. Øverbø, “Relativistic Atomic Form Factors and Photon Coherent Scattering Cross Sections,” Journal of Physical and Chemical Reference Data, vol. 8, no. 1, pp. 69–106, 1979.

[9] B. Cullity and S.R. Stock, Elements of X-ray Diffraction, 2001.

[10] A. Taylor and H. Sinclair, “On the Determination of Lattice Parameters by the Debye-Scherrer Method,” P Phys Soc, vol. 57, no. 320, pp. 126–135, 1945.

[11] V. Palamodov, “An analytic reconstruction for the Compton scattering tomography in a plane,” Inverse Problems, vol. 27, no. 12, p. 125004, 2011.

[12] M. Nguyen and T. Truong, “Inversion of a new circular-arc Radon transform for Compton scattering tomography,” Inverse Problems, vol. 26, no. 6, p. 065005, 2010.

[13] T. T. Truong, M. Nguyen, and H. Zaidi, “The mathematical foundations of 3D Compton scatter emission imaging,” International journal of biomedical imaging, vol. 2007, 2007.

[14] L. Hormander, “Fourier integral operators. I,” Acta Math-djursholm, vol. 127, no. 1, p. 79, 1971.

[15] G. Rigaud and B. N. Hahn, “3D Compton Scattering Imaging and Contour Reconstruction for a Class of Radon Transforms,” Inverse Probl, vol. 34, no. 7, p. 075004, 2018.

[16] A. Y. Ng, “Feature Selection, L 1 vs. L 2 Regularization, and Rotational Invariance,” p. 78.

[17] S. Gazzola and M. Landman, “Flexible GMRES for Total Variation Regularization,” BIT Numerical Mathematics, 2019.

[18] V. P. Krishnan and E. Quinto, “Microlocal Analysis in Tomography,” Handbook of Mathematical Methods in Imaging, pp. 1–50, 2014.

[19] P. Hansen and J. Jørgensen, “Total Variation and Tomographic Imaging from Projections.”

[20] H. Rezaee, P. Rothschild, B. Tracey, and E. L. Miller, “On the Fusion of Energy Resolved Scatter and Attenuation Data for Limited-view X-ray Materials Characterization with Application to Security Screening,” IEEE Transactions on Computational Imaging, 2019.

[21] A. Desmal et al., “Sparse-View Compton Scatter Tomography with Energy Resolved Data: Experimental and Simulation Results,” vol. 10187, p. 1018707, 2017. DOI: 10.1117/12.2266688.

[22] Y. Yuan, B. Tracey, and E. Miller, “Robust X-ray Based Material Identification Using Multi-energy Sinogram Decomposition,” pp. 98470V-98470V–13, 2016.

[23] B. H. Tracey and E. L. Miller, “Stabilizing Dual-energy X-ray Computed Tomography Reconstructions Using Patch-based Regularization,” Inverse Problems, vol. 31, no. 10, p. 105004, 2015.

[24] B. H. Tracey and E. L. Miller, “Geometric Image Formation for Target Identification in Multi-energy computed tomography,” vol. 8746, p. 87460T, 2013. DOI:10.1117/12.2020668.



Project R4-B.2

[25] O. Semerci, N. Hao, M. E. Kilmer, and E. L. Miller, “Tensor-Based Formulation and Nuclear Norm Regularization for Multienergy Computed Tomography,” IEEE Transactions on Image Processing, vol. 23, no. 4, pp. 1678–1693, 2014.

[26] O. Semerci and E. L. Miller, “A Parametric Level-Set Approach to Simultaneous Object Identification and Background Reconstruction for Dual-Energy Computed Tomography,” IEEE Transactions on Image Processing, vol. 21, no. 5, pp. 2719–2734, 2012.

[27] J. W. Webber and S. Holman, “Microlocal Analysis of a Spindle Transform,” Inverse Problems Imaging, vol. 13, no. 2, pp. 231–261, 2019.

[28] J. W. Webber and W. R. Lionheart, “Three-Dimensional Compton Scattering Tomography,” Inverse Problem, vol. 34, no. 8, p. 084001, 2018.



Project R4-B.2

This page intentionally left blank.



Project R4-B.2

Documents

I. PARTICIPANTS II. PROJECT DESCRIPTION