Plug-and-Play ADMM for MRI Reconstruction With Convex Nonconvex Sparse Regularization

Li, Jincheng; Li, Jinlan; Xie, Zhaoyang; Zou, Jian

doi:10.1109/access.2021.3124600

Cited by 7 publications

(3 citation statements)

References 53 publications

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“…The techniques for constructing the smoothed version of the convex sparse regularizer include but are not limited to Moreau envelope [16,28], Nesterov's smoothing [29], and infimal convolution smoothing [30]. CNC sparse regularization has shown excellent performance in signal denoising [24,31], medical image reconstruction [32][33][34][35], fault diagnosis [36,37], and other fields.…”

Section: Cnc Sparse Regularizationmentioning

confidence: 99%

Plug‐and‐play algorithms for convex non‐convex regularization: Convergence analysis and applications

Xu,

Qu,

Liu

et al. 2023

Math Methods in App Sciences

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When the sparse regularizer is convex and its proximal operator has a closed‐form, first‐order iterative algorithms based on proximal operators can effectively solve the sparse optimization problems. Recently, plug‐and‐play (PnP) algorithms have achieved significant success by incorporating advanced denoisers to replace the proximal operators in iterative algorithms. However, convex sparse regularizers such as the ‐norm tend to underestimate the large values within the sparse solutions. In contrast, the convex non‐convex (CNC) sparse regularization enables the non‐convex regularizer while preserving the convexity of the objective function. In this paper, we propose several PnP algorithms for solving the CNC sparse regularization model and discuss their convergence properties. Specifically, we first derive the proximal operator for CNC sparse regularization in iterative form and subsequently integrate it with several first‐order algorithms to yield different PnP algorithms. Then, based on the monotone operator theory, we prove that the proposed PnP algorithms are convergent under the condition that the data‐fidelity term is strongly convex and the residuals of the denoisers are contractive. We also emphasized the significance of strong convexity in the data‐fidelity term for the CNC sparse regularization model. Additionally, we demonstrate the superiority of the proposed PnP algorithms through extensive image restoration tasks.

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Section: Cnc Sparse Regularizationmentioning

confidence: 99%

Plug‐and‐play algorithms for convex non‐convex regularization: Convergence analysis and applications

Xu,

Qu,

Liu

et al. 2023

Math Methods in App Sciences

Self Cite

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show abstract

“…However, the proximal operator of

{\phi}_B&#x0005E;{GMC}(v)

cannot be expressed in closed form. Following the method in Li et al, 43 we solve () by PGD iteration.…”

Section: Admm Algorithm For Cnc‐gtv Modelmentioning

confidence: 99%

Diffusion optical tomography reconstruction based on convex–nonconvex graph total variation regularization

Xie

Liu

et al. 2022

Math Methods in App Sciences

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Graph total variation (GTV) is a powerful regularization tool for diffuse optical tomography (DOT) reconstruction since it combines the powerful representation ability of graph and the edge-preserving ability of total variation (TV) regularization. However, as everyone knows, the classical TV regularization trend underestimates the large edge values. In this paper, we propose a convex-nonconvex graph total variation (CNC-GTV) regularization for DOT reconstruction. In particular, we construct a nonconvex regularization by subtracting the generalized Huber function from the GTV regularization. We show that the global convexity of the objective function can be guaranteed by adjusting the nonconvex control parameters. Moreover, we present an alternating direction multiplier method (ADMM) to solve the proposed DOT reconstruction model. Numerical experiments show that the proposed model outperforms existing models in visual and numerical results.

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“…Moreover, within the framework of the iterative algorithm, theoretical guarantees for convergence are also provided. As a result, PnP algorithms have gained widespread adoption in various image tasks [7,8,[35][36][37][38][39][40].…”

Section: Introductionmentioning

confidence: 99%

Image Deblurring Based on Convex Non-Convex Sparse Regularization and Plug-and-Play Algorithm

Wang,

Xu,

et al. 2023

Algorithms

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Image deblurring based on sparse regularization has garnered significant attention, but there are still certain limitations that need to be addressed. For instance, convex sparse regularization tends to exhibit biased estimation, which can adversely impact the deblurring performance, while non-convex sparse regularization poses challenges in terms of solving techniques. Furthermore, the performance of the traditional iterative algorithm also needs to be improved. In this paper, we propose an image deblurring method based on convex non-convex (CNC) sparse regularization and a plug-and-play (PnP) algorithm. The utilization of CNC sparse regularization not only mitigates estimation bias but also guarantees the overall convexity of the image deblurring model. The PnP algorithm is an advanced learning-based optimization algorithm that surpasses traditional optimization algorithms in terms of efficiency and performance by utilizing the state-of-the-art denoiser to replace the proximal operator. Numerical experiments verify the performance of our proposed algorithm in image deblurring.

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Plug-and-Play ADMM for MRI Reconstruction With Convex Nonconvex Sparse Regularization

Cited by 7 publications

References 53 publications

Plug‐and‐play algorithms for convex non‐convex regularization: Convergence analysis and applications

Plug‐and‐play algorithms for convex non‐convex regularization: Convergence analysis and applications

Diffusion optical tomography reconstruction based on convex–nonconvex graph total variation regularization

Image Deblurring Based on Convex Non-Convex Sparse Regularization and Plug-and-Play Algorithm

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