Overlapping group sparsity on hyper-Laplacian prior of sparse angle CT reconstruction

Qi Ziwen; Kong Huihua; Li Jiaxin; Pan Jinxiao

doi:10.12086/oee.2023.230167

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Qi Z W, Kong H H, Li J X, et al. Overlapping group sparsity on hyper-Laplacian prior of sparse angle CT reconstruction[J]. Opto-Electron Eng, 2023, 50(10): 230167. doi: 10.12086/oee.2023.230167

Citation:

Qi Z W, Kong H H, Li J X, et al. Overlapping group sparsity on hyper-Laplacian prior of sparse angle CT reconstruction[J]. Opto-Electron Eng, 2023, 50(10): 230167. doi: 10.12086/oee.2023.230167

Overlapping group sparsity on hyper-Laplacian prior of sparse angle CT reconstruction

1.
School of Mathematics, North University of China, Taiyuan, Shanxi 030051, China
2.
Shanxi Key Laboratory of Signal Capturing & Processing, North University of China, Taiyuan, Shanxi 030051, China

Fund Project: Project supported by National Natural Science Foundation of China (62201520, 62103384, 62122070), and Basic Research Project of Shanxi Province Fund (202103021224190)

More Information

^*Corresponding author: huihuak@163.com

Received Date 10 July 2023

Revised Date 19 September 2023

Accepted Date 20 September 2023

Published Date 25 October 2023

Abstract

Abstract

For the sparse angle projection data, the problem of artifact and noise is easy to appear in the image reconstruction of computed tomography, which is difficult to meet the requirements of industrial and medical diagnosis. In this paper, a sparse angle CT iterative reconstruction algorithm based on overlapping group sparsity and hyper-Laplacian prior is proposed. The overlapping group sparsity reflects the sparsity of image gradient, and the overlapping cross relation between the adjacent elements is considered from the perspective of the image gradient. The hyper-Laplacian prior can accurately approximate the heavy-tailed distribution of the image gradient and improve the overall quality of the reconstructed image. The algorithm model proposed in this paper uses alternating direction multiplier method, principal component minimization method and gradient descent method to solve the objective function. The experimental results show that under the condition of the sparse angle CT reconstruction, the proposed algorithm has certain improvement in preserving structural details and suppressing noise and staircase artifacts generated in the process of image reconstruction.
- CT reconstruction /
- sparse angle /
- image gradient /
- overlapping group sparsity /
- hyper-Laplacian prior

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References

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Overview

Overview

X-ray computed tomography (CT) is an imaging technique to obtain the across section information of an object through X-ray projection measurement at different angles, which has been widely used in industry, clinical diagnosis and other fields. However, additional X-ray radiation during clinical examination can lead to cancer and other genetic changes. In order to reduce the dose of X-ray radiation, sparse angle projection is used to add the scanning interval and reduce the number of projection times, and a small amount of projection data is used to achieve image reconstruction. However, this method will reduce the quality of the reconstructed image, there will be more artifacts and noise, and it is difficult to meet the requirements of industrial and medical diagnosis. In order to improve the quality of reconstructed images under sparse sampling, a sparse angle CT reconstruction algorithm based on overlapping group sparsity and hyper-Laplacian prior is proposed in this paper. The sparse regular term of the overlapping group improves the sparsity of the image gradient. The structure information of the image gradient is used as the measurement standard of the image gradient sparsity, which fully considers the gradient information of the pixel neighborhood, and regroups the gradient information by two norms to increase the difference between the smooth region and the image edge region. Since the gradient of the image basically follows the heavy-tailed distribution, the hyper-Laplacian prior can accurately approximate the heavy tail distribute-on of the image gradient, this regular term can suppress the noise generated in the reconstruction process. Combining the advantages of the two regular terms, the algorithm can effectively overcome the staircase artifacts while recovering the edge of the image, and remove the noise generated in the reconstruction. In this paper, alternate direction multiplier method, principal component minimization method and gradient descent method are used to solve the objective function. The experimental data of the simulated mouse model and the clinical mouse model were used in this study. The peak signal-to-noise ratio (PSNR), normalized root-mean-square error (NRMSE) and structural similarity index (SSIM) were used as indicators to evaluate different algorithms, and regions of interest were added to compare the reconstructed images, so that the differences of different algorithms could be more clearly seen from the structural details of the mouse model. The experimental results show that the proposed algorithm has some improvements in preserving the details of image structure and suppressing noise and staircase artifacts in the process of image reconstruction.