Sparse-View Spectral CT Reconstruction Using Spectral Patch-Based Low-Rank Penalty

Abstract

Spectral computed tomography (CT) is a promising technique with the potential for improving lesion detection, tissue characterization, and material decomposition. In this paper, we are interested in kVp switching-based spectral CT that alternates distinct kVp X-ray transmissions during gantry rotation. This system can acquire multiple X-ray energy transmissions without additional radiation dose. However, only sparse views are generated for each spectral measurement; and the spectra themselves are limited in number. To address these limitations, we propose a penalized maximum likelihood method using spectral patch-based low-rank penalty, which exploits the self-similarity of patches that are collected at the same position in spectral images. The main advantage is that the relatively small number of materials within each patch allows us to employ the low-rank penalty that is less sensitive to intensity changes while preserving edge directions. In our optimization formulation, the cost function consists of the Poisson log-likelihood for X-ray transmission and the nonconvex patch-based low-rank penalty. Since the original cost function is difficult to minimize directly, we propose an optimization method using separable quadratic surrogate and concave convex procedure algorithms for the log-likelihood and penalty terms, which results in an alternating minimization that provides a computational advantage because each subproblem can be solved independently. We performed computer simulations and a real experiment using a kVp switching-based spectral CT with sparse-view measurements, and compared the proposed method with conventional algorithms. We confirmed that the proposed method improves spectral images both qualitatively and quantitatively. Furthermore, our GPU implementation significantly reduces the computational cost.

TICMR: Total Image Constrained Material Reconstruction via Nonlocal Total Variation Regularization for Spectral CT

“…In the result section, we compare TICMR with FBP and the following TV based material reconstruction $$Z^{*}=\text{arg }\underset{Z}{\text{min}}\frac{1}{2}{false\Vert AZB-Pfalse\Vert }_W^2+\lambda {false|\nabla Zfalse|}_1.$$ $$\mathrm{normals}.\mathrm{normalt}.ZC=D,L\le Z\le U.$$ Note that in terms of the regularization in (17), the alternative strategies can be used, such as tensor framelet transform (as a natural high-order generalization of isotropic TV) [3], [11], [29]–[31], and low-rank models [7], [10], [15], [32], [33]. …”

“…It can be determined in a two-step procedure, i.e., image reconstruction for spectral images and then material decomposition from these spectral images to material compositions [3], [6]–[16], or alternatively material-specific sinogram decomposition and then material reconstruction [4], [17]–[19]. Various iterative reconstruction models have been developed [20], with energy-by-energy reconstruction [3], [4], [9], [11], [17]–[19] and joint reconstruction [7], [10], [15], [16], such as total variation (TV) sparsity [14], [16], HYPR algorithm [8], tight frame sparsity [3], [11], bilateral filtration [12], [13], patch-based low-rank model [15], rank-and-sparsity decomposition model [7] and its tensor version [10]. In order to fully utilize the image similarity in the spectral dimension, the joint reconstruction is a natural formulation [7], [10], [15], [16].…”

“…Various iterative reconstruction models have been developed [20], with energy-by-energy reconstruction [3], [4], [9], [11], [17]–[19] and joint reconstruction [7], [10], [15], [16], such as total variation (TV) sparsity [14], [16], HYPR algorithm [8], tight frame sparsity [3], [11], bilateral filtration [12], [13], patch-based low-rank model [15], rank-and-sparsity decomposition model [7] and its tensor version [10]. In order to fully utilize the image similarity in the spectral dimension, the joint reconstruction is a natural formulation [7], [10], [15], [16]. Although the image intensity with different energies can be significantly different, the global sparsity, such as low-rank models, is efficient to characterize the spectral similarity.…”

Numerical observer for atherosclerotic plaque classification in spectral computed tomography

“…Furthermore, MECT-PC has the ability to decompose more than two materials, as more than one K-edge contrast medium can be simultaneously imaged and distinguished using four or more energy thresholds or windows. 9,59 In this case, the proposed framework can be extended to support multiclass discrimination tasks or multiple-decision L-class problem with L > 2, where the data are to be assigned to one of L possible hypotheses or the underlying classes. Thus, multiple discriminant functions and partitioning rules are required to support multiple materialclassification tasks.…”

Iterative Low-Dose CT Reconstruction With Priors Trained by Artificial Neural Network

“…A potential function was designed for the difference between neighboring pixels and minimized under data fidelity. Priors such as total variation (TV) or non-local patch-based priors have shown promising results in CT reconstruction with insufficient data, and some if it has already been deployed in commercial software [5][6]. …”