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Volume 10 Issue 11
Nov.  2023

IEEE/CAA Journal of Automatica Sinica

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Article Navigation >  IEEE/CAA Journal of Automatica Sinica  > 2023  >  10(11): 2136-2153
B. S. Shi and  K. X. Liu,  “Regularization by multiple dual frames for compressed sensing magnetic resonance imaging with convergence analysis,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 11, pp. 2136–2153, Nov. 2023. doi: 10.1109/JAS.2023.123543
Citation: B. S. Shi and  K. X. Liu,  “Regularization by multiple dual frames for compressed sensing magnetic resonance imaging with convergence analysis,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 11, pp. 2136–2153, Nov. 2023. doi: 10.1109/JAS.2023.123543
shu

Regularization by Multiple Dual Frames for Compressed Sensing Magnetic Resonance Imaging With Convergence Analysis

doi: 10.1109/JAS.2023.123543
Funds:  This work was supported in part by the National Natural Science Foundation of China (62371414, 61901406), the Hebei Natural Science Foundation (F2020203025), the Young Talent Program of Universities and Colleges in Hebei Province (BJ2021044), the Hebei Key Laboratory Project (202250701010046), and the Central Government Guides Local Science and Technology Development Fund Projects (216Z1602G)
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    Abstract

  • Plug-and-play priors are popular for solving ill-posed imaging inverse problems. Recent efforts indicate that the convergence guarantee of the imaging algorithms using plug-and-play priors relies on the assumption of bounded denoisers. However, the bounded properties of existing plugged Gaussian denoisers have not been proven explicitly. To bridge this gap, we detail a novel provable bounded denoiser termed as BMDual, which combines a trainable denoiser using dual tight frames and the well-known block-matching and 3D filtering (BM3D) denoiser. We incorporate multiple dual frames utilized by BMDual into a novel regularization model induced by a solver. The proposed regularization model is utilized for compressed sensing magnetic resonance imaging (CSMRI). We theoretically show the bound of the BMDual denoiser, the bounded gradient of the CSMRI data-fidelity function, and further demonstrate that the proposed CSMRI algorithm converges. Experimental results also demonstrate that the proposed algorithm has a good convergence behavior, and show the effectiveness of the proposed algorithm.

     

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    Highlights

    • We propose a trainable bounded Gaussian denoiser
    • We propose a novel regularization model using multiple dual frames
    • We prove the convergence of the proposed CSMRI algorithm
    • Our algorithm achieves better reconstructions than existing CSMRI algorithms

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