NDLI: An Accelerated Proximal Gradient Algorithm for Frame-Based Image Restoration via the Balanced Approach

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An Accelerated Proximal Gradient Algorithm for Frame-Based Image Restoration via the Balanced Approach

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Yun, Sangwoon Toh, Kim-Chuan Shen, Zuowei
Copyright Year	2011
Abstract	Frame-based image restoration by using the balanced approach has been developed over the last decade. Many recently developed algorithms for image restoration can be viewed as an acceleration of the proximal forward-backward splitting algorithm. Accelerated proximal gradient (APG) algorithms studied by Nesterov, Nemirovski, and others have been demonstrated to be efficient in solving various regularized convex optimization problems arising in compressed sensing, machine learning, and control. In this paper, we adapt the APG algorithm to solve the $\ell_1$-regularized linear least squares problem in the balanced approach in frame-based image restoration. This algorithm terminates in $O(1/\sqrt{\epsilon})$ iterations with an $\epsilon$-optimal solution, and we demonstrate that this single algorithmic framework can universally handle several image restoration problems, such as image deblurring, denoising, inpainting, and cartoon-texture decomposition. Our numerical results suggest that the APG algorithms are efficient and robust in solving large-scale image restoration problems. The algorithms we implemented are able to restore $512\times512$ images in various image restoration problems in less than 50 seconds on a modest PC. We also compare the numerical performance of our proposed algorithms applied to image restoration problems by using one frame-based system with that by using cartoon and texture systems for image deblurring, denoising, and inpainting.
Starting Page	573
Ending Page	596
Page Count	24
File Format	PDF
DOI	10.1137/090779437
e-ISSN	19364954
Journal	SIAM Journal on Imaging Sciences (SJISBI)
Issue Number	2
Volume Number	4
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2011-06-07
Access Restriction	Subscribed
Subject Keyword	synthesis based approach proximal gradient algorithms Wavelets balanced approach image restoration $\ell_1$-regularized convex minimization Image processing analysis based approach iteration complexity Convex programming Large-scale problems
Content Type	Text
Resource Type	Article

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