Nonconvex ${{L_ {{1/2}}}} $-Regularized Nonlocal Self-similarity Denoiser for Compressive Sensing based CT Reconstruction

TL;DR

This paper introduces a novel nonconvex $L_{1/2}$-regularized nonlocal self-similarity denoiser for CT reconstruction, improving image quality from sparse-view data by integrating low-rank approximation and group sparse coding within an ADMM framework.

Contribution

It develops a new $L_{1/2}$-regularized NSS denoiser that combines low-rank minimization with group sparse coding for enhanced CT image reconstruction from limited data.

Findings

Outperforms existing methods on clinical CT images

Achieves higher image quality with fewer projections

Demonstrates effectiveness of $L_{1/2}$ regularization in CT denoising

Abstract

Compressive sensing (CS) based computed tomography (CT) image reconstruction aims at reducing the radiation risk through sparse-view projection data. It is usually challenging to achieve satisfying image quality from incomplete projections. Recently, the nonconvex ${{L_ {{1/2}}}} $-norm has achieved promising performance in sparse recovery, while the applications on imaging are unsatisfactory due to its nonconvexity. In this paper, we develop a ${{L_ {{1/2}}}} $-regularized nonlocal self-similarity (NSS) denoiser for CT reconstruction problem, which integrates low-rank approximation with group sparse coding (GSC) framework. Concretely, we first split the CT reconstruction problem into two subproblems, and then improve the CT image quality furtherly using our ${{L_ {{1/2}}}} $-regularized NSS denoiser. Instead of optimizing the nonconvex problem under the perspective of GSC, we particularly reconstruct CT image via low-rank minimization based on two simple yet essential schemes, which build the equivalent relationship between GSC based denoiser and low-rank minimization. Furtherly, the weighted singular value thresholding (WSVT) operator is utilized to optimize the resulting nonconvex ${{L_ {{1/2}}}} $ minimization problem. Following this, our proposed denoiser is integrated with the CT reconstruction problem by alternating direction method of multipliers (ADMM) framework. Extensive experimental results on typical clinical CT images have demonstrated that our approach can further achieve better performance than popular approaches.