Accelerated Proximal Iterative re-Weighted $\ell_1$ Alternating Minimization for Image Deblurring
The quadratic penalty alternating minimization (AM) method is widely used for solving the convex $\ell_1$ total variation (TV) image deblurring problem. However, quadratic penalty AM for solving the nonconvex nonsmooth $\ell_p$, $0 < p < 1$ TV image deblurring problems is less studied. In this...
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| creator | Adam, Tarmizi Malyshev, Alexander Hassan, Mohd Fikree Mohamed, Nur Syarafina Salam, Md Sah Hj |
| description | The quadratic penalty alternating minimization (AM) method is widely used for
solving the convex $\ell_1$ total variation (TV) image deblurring problem.
However, quadratic penalty AM for solving the nonconvex nonsmooth $\ell_p$, $0
< p < 1$ TV image deblurring problems is less studied. In this paper, we
propose two algorithms, namely proximal iterative re-weighted $\ell_1$ AM
(PIRL1-AM) and its accelerated version, accelerated proximal iterative
re-weighted $\ell_1$ AM (APIRL1-AM) for solving the nonconvex nonsmooth
$\ell_p$ TV image deblurring problem. The proposed algorithms are derived from
the proximal iterative re-weighted $\ell_1$ (IRL1) algorithm and the proximal
gradient algorithm. Numerical results show that PIRL1-AM is effective in
retaining sharp edges in image deblurring while APIRL1-AM can further provide
convergence speed up in terms of the number of algorithm iterations and
computational time. |
| doi_str_mv | 10.48550/arxiv.2309.05204 |
| format | Article |
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solving the convex $\ell_1$ total variation (TV) image deblurring problem.
However, quadratic penalty AM for solving the nonconvex nonsmooth $\ell_p$, $0
< p < 1$ TV image deblurring problems is less studied. In this paper, we
propose two algorithms, namely proximal iterative re-weighted $\ell_1$ AM
(PIRL1-AM) and its accelerated version, accelerated proximal iterative
re-weighted $\ell_1$ AM (APIRL1-AM) for solving the nonconvex nonsmooth
$\ell_p$ TV image deblurring problem. The proposed algorithms are derived from
the proximal iterative re-weighted $\ell_1$ (IRL1) algorithm and the proximal
gradient algorithm. Numerical results show that PIRL1-AM is effective in
retaining sharp edges in image deblurring while APIRL1-AM can further provide
convergence speed up in terms of the number of algorithm iterations and
computational time.</description><identifier>DOI: 10.48550/arxiv.2309.05204</identifier><language>eng</language><subject>Mathematics - Optimization and Control</subject><creationdate>2023-09</creationdate><rights>http://creativecommons.org/licenses/by/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,778,883</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2309.05204$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2309.05204$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Adam, Tarmizi</creatorcontrib><creatorcontrib>Malyshev, Alexander</creatorcontrib><creatorcontrib>Hassan, Mohd Fikree</creatorcontrib><creatorcontrib>Mohamed, Nur Syarafina</creatorcontrib><creatorcontrib>Salam, Md Sah Hj</creatorcontrib><title>Accelerated Proximal Iterative re-Weighted $\ell_1$ Alternating Minimization for Image Deblurring</title><description>The quadratic penalty alternating minimization (AM) method is widely used for
solving the convex $\ell_1$ total variation (TV) image deblurring problem.
However, quadratic penalty AM for solving the nonconvex nonsmooth $\ell_p$, $0
< p < 1$ TV image deblurring problems is less studied. In this paper, we
propose two algorithms, namely proximal iterative re-weighted $\ell_1$ AM
(PIRL1-AM) and its accelerated version, accelerated proximal iterative
re-weighted $\ell_1$ AM (APIRL1-AM) for solving the nonconvex nonsmooth
$\ell_p$ TV image deblurring problem. The proposed algorithms are derived from
the proximal iterative re-weighted $\ell_1$ (IRL1) algorithm and the proximal
gradient algorithm. Numerical results show that PIRL1-AM is effective in
retaining sharp edges in image deblurring while APIRL1-AM can further provide
convergence speed up in terms of the number of algorithm iterations and
computational time.</description><subject>Mathematics - Optimization and Control</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotjztPwzAUhb0woMIPYMJD1wQ7tmN7jMorUhEMlViQIj9ugiUnQaZUhV-PU1ju0T3n6EgfQleUlFwJQW5MOoZDWTGiSyIqws-RaZyDCMnsweOXNB_DaCJu94sTDoATFK8QhvclXr9BjB1d4ybmfMqFacBPYQpj-MnPPOF-TrgdzQD4Fmz8Sik3LtBZb-InXP7rCu3u73abx2L7_NBumm1hasnzYX3vrNXUS0lrDdoyIpmupVCEg5OOGsO4rLVivNaV0JYay8B7RZT3jq3Q9d_sibH7SBkkfXcLa3diZb8K9097</recordid><startdate>20230910</startdate><enddate>20230910</enddate><creator>Adam, Tarmizi</creator><creator>Malyshev, Alexander</creator><creator>Hassan, Mohd Fikree</creator><creator>Mohamed, Nur Syarafina</creator><creator>Salam, Md Sah Hj</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20230910</creationdate><title>Accelerated Proximal Iterative re-Weighted $\ell_1$ Alternating Minimization for Image Deblurring</title><author>Adam, Tarmizi ; Malyshev, Alexander ; Hassan, Mohd Fikree ; Mohamed, Nur Syarafina ; Salam, Md Sah Hj</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a674-a63ffcbb91d77169e9b30739675804ec7c1aa3476983469259b1ab3edd808ddc3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Mathematics - Optimization and Control</topic><toplevel>online_resources</toplevel><creatorcontrib>Adam, Tarmizi</creatorcontrib><creatorcontrib>Malyshev, Alexander</creatorcontrib><creatorcontrib>Hassan, Mohd Fikree</creatorcontrib><creatorcontrib>Mohamed, Nur Syarafina</creatorcontrib><creatorcontrib>Salam, Md Sah Hj</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Adam, Tarmizi</au><au>Malyshev, Alexander</au><au>Hassan, Mohd Fikree</au><au>Mohamed, Nur Syarafina</au><au>Salam, Md Sah Hj</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Accelerated Proximal Iterative re-Weighted $\ell_1$ Alternating Minimization for Image Deblurring</atitle><date>2023-09-10</date><risdate>2023</risdate><abstract>The quadratic penalty alternating minimization (AM) method is widely used for
solving the convex $\ell_1$ total variation (TV) image deblurring problem.
However, quadratic penalty AM for solving the nonconvex nonsmooth $\ell_p$, $0
< p < 1$ TV image deblurring problems is less studied. In this paper, we
propose two algorithms, namely proximal iterative re-weighted $\ell_1$ AM
(PIRL1-AM) and its accelerated version, accelerated proximal iterative
re-weighted $\ell_1$ AM (APIRL1-AM) for solving the nonconvex nonsmooth
$\ell_p$ TV image deblurring problem. The proposed algorithms are derived from
the proximal iterative re-weighted $\ell_1$ (IRL1) algorithm and the proximal
gradient algorithm. Numerical results show that PIRL1-AM is effective in
retaining sharp edges in image deblurring while APIRL1-AM can further provide
convergence speed up in terms of the number of algorithm iterations and
computational time.</abstract><doi>10.48550/arxiv.2309.05204</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Optimization and Control |
| title | Accelerated Proximal Iterative re-Weighted $\ell_1$ Alternating Minimization for Image Deblurring |
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