Smoothing L0- and L1-Norm regularizers and their relations to non-local means for CT reconstruction

Yueyang Teng; Qing Guo; Ge Wang

doi:10.1117/12.2530522

10 September 2019 Smoothing L₀- and L₁-Norm regularizers and their relations to non-local means for CT reconstruction

Yueyang Teng, Qing Guo, Ge Wang

Proceedings Volume 11113, Developments in X-Ray Tomography XII; 111131M (2019) https://doi.org/10.1117/12.2530522
Event: SPIE Optical Engineering + Applications, 2019, San Diego, California, United States

Abstract

Total variation based on the L₀− and L₁−norm regularizers is a popular and powerful method for computed tomography (CT) reconstruction from noisy data. However their solutions are difficult to compute because of non-differentiability and even discontinuity. In this paper, we propose smoothing L₀- and L₁-norm regularizers to approximate the original norms. Also, we provide two expectation maximization (EM) like iterative algorithms, which have properties similar to that of the EM algorithm, including the monotonous decrement of the cost function and the self-constraint within a non-negative space. Finally, we build the relationship between the non-local means (NLM) methods and the above methods. The simulated CT projections are used to evaluate the performance of the proposed algorithms. The results show the superiority of the new methods over the existing methods in terms of noise suppression and computational cost.

Citation Download Citation

Yueyang Teng, Qing Guo, and Ge Wang "Smoothing L₀- and L₁-Norm regularizers and their relations to non-local means for CT reconstruction", Proc. SPIE 11113, Developments in X-Ray Tomography XII, 111131M (10 September 2019); https://doi.org/10.1117/12.2530522

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