Coded apertures for x-ray scatter imaging

Brady, David J.; Marks, Daniel L.; MacCabe, Kenneth P.; O'Sullivan, Joseph A.

doi:10.1364/ao.52.007745

Cited by 35 publications

(22 citation statements)

References 17 publications

(20 reference statements)

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“…The array has 128 pixels and 64 energy channels. The rays leaving the object volume are incident on a coded aperture [13], [11], which allows for multiplexed measurement without the need for a rotating gantry.…”

Section: Resultsmentioning

confidence: 99%

Spectrally grouped total variation reconstruction for scatter imaging using ADMM

Odinaka

Kaganovsky

Greenberg

et al. 2015

2015 IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC)

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Abstract-We consider X-ray coherent scatter imaging, where the goal is to reconstruct momentum transfer profiles (spectral distributions) at each spatial location from multiplexed measurements of scatter. Each material is characterized by a unique momentum transfer profile (MTP) which can be used to discriminate between different materials. We propose an iterative image reconstruction algorithm based on a Poisson noise model that can account for photon-limited measurements as well as various second order statistics of the data. To improve image quality, previous approaches use edge-preserving regularizers to promote piecewise constancy of the image in the spatial domain while treating each spectral bin separately. Instead, we propose spectrally grouped regularization that promotes piecewise constant images along the spatial directions but also ensures that the MTPs of neighboring spatial bins are similar, if they contain the same material. We demonstrate that this group regularization results in improvement of both spectral and spatial image quality. We pursue an optimization transfer approach where convex decompositions are used to lift the problem such that all hypervoxels can be updated in parallel and in closed-form. The group penalty introduces a challenge since it is not directly amendable to these decompositions. We use the alternating directions method of multipliers (ADMM) to replace the original problem with an equivalent sequence of sub-problems that are amendable to convex decompositions, leading to a highly parallel algorithm. We demonstrate the performance on real data.

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Section: Resultsmentioning

confidence: 99%

Spectrally grouped total variation reconstruction for scatter imaging using ADMM

Odinaka

Kaganovsky

Greenberg

et al. 2015

2015 IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC)

Self Cite

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“…2 a block-unblock coded aperture is feasible [23,30]. Specifically, the blocking elements of these coded apertures can be fabricated using tungsten, since this material can stop an x-ray beam, resulting in low fabrication costs [31][32][33]. since F H F = FF H = I, T(z p ) is a diagonal orthogonal matrix, and R r=1 S r S r = I.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Exact Crystalline Structure Recovery in X-ray Crystallography from Coded Diffraction Patterns

Pinilla,

Bacca,

Vargas

et al. 2019

Preprint

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X-ray crystallography (XC) is an experimental technique used to determine three-dimensional crystalline structures. The acquired data in XC, called diffraction patterns, is the Fourier magnitudes of the unknown crystalline structure. To estimate the crystalline structure from its diffraction patterns, we propose to modify the traditional system by including an optical element called coded aperture which modulates the diffracted field to acquire coded diffraction patterns (CDP). For the proposed coded system, in contrast with the traditional, we derive exact reconstruction guarantees for the crystalline structure from CDP (up to a global shift phase). Additionally, exploiting the fact that the crystalline structure can be sparsely represented in the Fourier domain, we develop an algorithm to estimate the crystal structure from CDP. We show that this method requires 50% fewer measurements to estimate the crystal structure in comparison with its competitive alternatives. Specifically, the proposed method is able to reduce the exposition time of the crystal, implying that under the proposed setup, its structural integrity is less affected in comparison with the traditional. We discuss further implementation of imaging devices that exploits this theoretical coded system.

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“…The joint image recovery problem, however, has remained largely avoided as authors focus on scatter density alone. For example, the attenuation image has been trivialized as constant [12], [13] or negligible [11], [14], [15]. Since both scatter density and attenuation are media dependent, joint image estimation could also improve object identification [14].…”

Section: Introductionmentioning

confidence: 99%

Iterative Algorithms for Joint Scatter and Attenuation Estimation From Broken Ray Transform Data

Walker,

O'Sullivan

2020

Preprint

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The single-scatter approximation is fundamental in many tomographic imaging problems including x-ray scatter imaging and optical scatter imaging for certain media. In all cases, noisy measurements are affected by both local scatter events and nonlocal attenuation. Prior works focus on reconstructing one of two images: scatter density or total attenuation. However, both images are media specific and useful for object identification.Nonlocal effects of the attenuation image on the data are summarized by the broken ray transform (BRT). While analytic inversion formulas exist, poor conditioning of the inverse problem is only exacerbated by noisy measurements and sampling errors. This has motivated interest in the related star transforms incorporating BRT measurements from multiple source-detector pairs. However, all analytic methods operate on the log of the data. For media comprising regions with no scatter a new approach is required.We are the first to present a joint estimation algorithm based on Poisson data models for a single-scatter measurement geometry. Monotonic reduction of the log-likelihood function is guaranteed for our iterative algorithm while alternating image updates. We also present a fast algorithm for computing the discrete BRT forward operator. Our generalized approach can incorporate both transmission and scatter measurements from multiple source-detector pairs. Transmission measurements resolve low-frequency ambiguity in the joint image estimation problem, while multiple scatter measurements resolve the attenuation image. The benefits of joint estimation, over single-image estimation, vary with problem scaling. Our results quantify these benefits and should inform design of future acquisition systems.

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Coded apertures for x-ray scatter imaging

Cited by 35 publications

References 17 publications

Spectrally grouped total variation reconstruction for scatter imaging using ADMM

Spectrally grouped total variation reconstruction for scatter imaging using ADMM

Exact Crystalline Structure Recovery in X-ray Crystallography from Coded Diffraction Patterns

Iterative Algorithms for Joint Scatter and Attenuation Estimation From Broken Ray Transform Data

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