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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.<\/jats:p>","DOI":"10.1137\/090779437","type":"journal-article","created":{"date-parts":[[2011,6,7]],"date-time":"2011-06-07T18:19:40Z","timestamp":1307470780000},"page":"573-596","source":"Crossref","is-referenced-by-count":60,"title":["An Accelerated Proximal Gradient Algorithm for Frame-Based Image Restoration via the Balanced Approach"],"prefix":"10.1137","volume":"4","author":[{"given":"Zuowei","family":"Shen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kim-Chuan","family":"Toh","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sangwoon","family":"Yun","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2011,6,7]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/080716542"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/090756855"},{"key":"R3","doi-asserted-by":"crossref","unstructured":"S. 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