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A hybrid statistical sampling and iterative regularization method in sparse-view computed tomography

Huiying Li, Yizhuang Song

Abstract

Sparse-view computed tomography (CT) is an effective method to reduce the radiation exposure in medical imaging. To reduce the severe streaking artifacts that occur in reconstructed images due to violation of the Nyquist/Shannon sampling criterion, regularization is widely used to minimize the cost function. However, the iterative methods may lead to the accumulation and propagation of errors, which adversely affects the restoration of image details and textures. In this paper, we propose a hybrid model that integrates statistical sampling with iterative regularization to simultaneously shorten the sampling time and enhance the reconstruction quality. The proposed method is validated using three datasets: the Shepp-Logan phantom, the actual walnut X-ray projections provided by the Finnish Inverse Problems Society, and the clinical lung CT images.

A hybrid statistical sampling and iterative regularization method in sparse-view computed tomography

Abstract

Sparse-view computed tomography (CT) is an effective method to reduce the radiation exposure in medical imaging. To reduce the severe streaking artifacts that occur in reconstructed images due to violation of the Nyquist/Shannon sampling criterion, regularization is widely used to minimize the cost function. However, the iterative methods may lead to the accumulation and propagation of errors, which adversely affects the restoration of image details and textures. In this paper, we propose a hybrid model that integrates statistical sampling with iterative regularization to simultaneously shorten the sampling time and enhance the reconstruction quality. The proposed method is validated using three datasets: the Shepp-Logan phantom, the actual walnut X-ray projections provided by the Finnish Inverse Problems Society, and the clinical lung CT images.
Paper Structure (12 sections, 3 theorems, 65 equations, 13 figures, 6 tables, 3 algorithms)

This paper contains 12 sections, 3 theorems, 65 equations, 13 figures, 6 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. The Bayesian-Variational hybrid model
  3. The nonlinear weighted anisotropic TV-Gaussian Bayesian model
  4. The structure of NWATG priors
  5. Theoretical properties of the NWATG prior
  6. Reconstruction method incorporating prior knowledge
  7. Experiments
  8. Experiment setup
  9. The reconstruction of NWATG statistical model
  10. The reconstruction of the hybrid model
  11. Discuss
  12. Conclusions and future works

Key Result

lemma 1

The regularization functional $\hbox{R}:\mathcal{X}\to\mathbb{R}$ satisfies the following properties: (1) For any $\mu\in\mathcal{X}$, $\hbox{R}(\mu)$ is bounded from below, and without loss of generality we can simply assume $\hbox{R}(\mu)\ge 0$. (2) For any $\delta>0$, there exists $M=M(\delta)>0$ for all $\mu_1,\mu_2\in\mathcal{X}$ with $\max\{\|\mu_1\|_{\mathcal{X}},\|\mu_2\|_{\mathcal{X}}\}\l

Figures (13)

  • Figure 1: The segmentation of ROI. We take the segmentation of the Shepp-Logan image ROI as an example. $\hbox{R}_1=\hbox{R}_{11}\cup \hbox{R}_{12}\cup \hbox{R}_{13}\cup \hbox{R}_{14}$.
  • Figure 2: Experimental data and corresponding ROIs. The top row displays (from left to right) the Shepp-Logan phantom with a simulated circular lesion, the actual walnut image and a clinical lung image, and the bottom row presents the corresponding ROIs. The pixel dimensions of the ROIs are 32$\times$32, 10$\times$10, and 20$\times$20, respectively.
  • Figure 3: Reference images and corresponding ROIs. Arranged left to right are the reference images for the Shepp-Logan phantom, the walnut projection, and the clinical lung CT image, along with their corresponding ROIs. The reference images (top row) are generated using the generalized Tikhonov regularization with parameters 200, 10 and 10 respectively. In the Shepp-Logan case, the projection data contains 0.5% Gaussian white noise.
  • Figure 4: The CM estimate from MCMC sampling within the ROI of Shepp-Logan phantom. The left is the initial value, and the right is the CM estimate. The image size is 32$\times$32.
  • Figure 5: The CM estimate from MCMC sampling within the ROI of walnut image. The left is the initial value, and the right is the CM estimate. The image size is 10$\times$10.
  • ...and 8 more figures

Theorems & Definitions (5)

  • lemma 1
  • proof
  • theorem 1
  • theorem 2
  • remark 1