Alternating Iteration for $l_{p}$ ( $0) Regularized CT Reconstruction

IEEE Access

Chuang Miao¹  Hengyong Yu² 

[1] Department of Biomedical Engineering, Wake Forest University School of Medicine, Winston-Salem, NC, USA;Department of Electrical and Computer Engineering, University of Massachusetts Lowell, Lowell, MA, USA;

关键词: Compressive sensing;    $l_{p}$ regularization;    computed tomography;    image reconstruction;    least square solution;    alternating iteration;   

DOI  :  10.1109/ACCESS.2016.2596704

来源: DOAJ

【 摘 要 】

The l_p (0 <; p <; 1) regularization has attracted a great attention in the compressive sensing field, because it can obtain sparser solutions than the well-known l₁ regularization. Recently, we developed an approximate general analytic thresholding representation for any lp regularization with 0 <; p <; 1. The derived thresholding representations are exact for the well-known soft-threshold filtering for l₁ regularization and the hard-threshold filtering for l₀ regularization. Because the lp regularization is a nonconvex problem, an iterative algorithm can only converge to local optima instead of the global optimum. In this paper, we propose an alternating iteration algorithm for computed tomography reconstruction in a thresholding form based on our general analytic thresholding representation for better convergent properties. The alternating iteration algorithm alternatively minimizes one l₁ and one l_p (0 <; p <; 1) regularized objective functions. While the lp regularization can help to find a sparser solution, the l₁ regularization can help to monitor the solution not away from the global optimum. Both numerical simulations and phantom experiments are performed to evaluate the proposed alternating iteration algorithm. Compared with the l_p (0 <; p <; 1) regularization using a single p, the proposed alternating iteration algorithm reduces more data measurements for accurate reconstruction and is more robust for projection noise.

【 授权许可】

Unknown