Sparse Regularization With Reverse Sorted Sum of Squares via an Unrolled Difference-of-Convex Approach
This paper proposes a sparse regularization method with a novel sorted regularization function. Sparse regularization is commonly used to solve underdetermined inverse problems. Traditional sparse regularization functions, such as <inline-formula><tex-math notation="LaTeX">$L_{...
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| Format: | Article |
| Language: | English |
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IEEE
2025-01-01
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| Series: | IEEE Open Journal of Signal Processing |
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| Online Access: | https://ieeexplore.ieee.org/document/10840312/ |
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| author | Takayuki Sasaki Kazuya Hayase Masaki Kitahara Shunsuke Ono |
| author_facet | Takayuki Sasaki Kazuya Hayase Masaki Kitahara Shunsuke Ono |
| author_sort | Takayuki Sasaki |
| collection | DOAJ |
| description | This paper proposes a sparse regularization method with a novel sorted regularization function. Sparse regularization is commonly used to solve underdetermined inverse problems. Traditional sparse regularization functions, such as <inline-formula><tex-math notation="LaTeX">$L_{1}$</tex-math></inline-formula>-norm, suffer from problems like amplitude underestimation and vanishing perturbations. The reverse ordered weighted <inline-formula><tex-math notation="LaTeX">$L_{1}$</tex-math></inline-formula>-norm (ROWL) addresses these issues but introduces new challenges. These include developing an algorithm grounded in theory, not heuristics, reducing computational complexity, enabling the automatic determination of numerous parameters, and ensuring the number of iterations remains feasible. In this study, we propose a novel sparse regularization function called the reverse sorted sum of squares (RSSS) and then construct an unrolled algorithm that addresses both the aforementioned two problems and these four challenges. The core idea of our proposed method lies in transforming the optimization problem into a difference-of-convex programming problem, for which solutions are known. In experiments, we apply the RSSS regularization method to image deblurring and super-resolution tasks and confirmed its superior performance compared to conventional methods, all with feasible computational complexity. |
| format | Article |
| id | doaj-art-68f9e0068ea843dab7879b66eaaccd1a |
| institution | Kabale University |
| issn | 2644-1322 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Open Journal of Signal Processing |
| spelling | doaj-art-68f9e0068ea843dab7879b66eaaccd1a2025-02-11T00:01:49ZengIEEEIEEE Open Journal of Signal Processing2644-13222025-01-016576710.1109/OJSP.2025.352931210840312Sparse Regularization With Reverse Sorted Sum of Squares via an Unrolled Difference-of-Convex ApproachTakayuki Sasaki0https://orcid.org/0000-0002-0504-557XKazuya Hayase1https://orcid.org/0009-0000-0856-4239Masaki Kitahara2https://orcid.org/0009-0009-4260-1174Shunsuke Ono3https://orcid.org/0000-0001-7890-5131NTT Corporation, Yokosuka, JapanNTT Corporation, Yokosuka, JapanNTT Corporation, Yokosuka, JapanInstitute of Science Tokyo, Yokohama, JapanThis paper proposes a sparse regularization method with a novel sorted regularization function. Sparse regularization is commonly used to solve underdetermined inverse problems. Traditional sparse regularization functions, such as <inline-formula><tex-math notation="LaTeX">$L_{1}$</tex-math></inline-formula>-norm, suffer from problems like amplitude underestimation and vanishing perturbations. The reverse ordered weighted <inline-formula><tex-math notation="LaTeX">$L_{1}$</tex-math></inline-formula>-norm (ROWL) addresses these issues but introduces new challenges. These include developing an algorithm grounded in theory, not heuristics, reducing computational complexity, enabling the automatic determination of numerous parameters, and ensuring the number of iterations remains feasible. In this study, we propose a novel sparse regularization function called the reverse sorted sum of squares (RSSS) and then construct an unrolled algorithm that addresses both the aforementioned two problems and these four challenges. The core idea of our proposed method lies in transforming the optimization problem into a difference-of-convex programming problem, for which solutions are known. In experiments, we apply the RSSS regularization method to image deblurring and super-resolution tasks and confirmed its superior performance compared to conventional methods, all with feasible computational complexity.https://ieeexplore.ieee.org/document/10840312/Deep unrollingdifference-of-convexinverse problemnon-convex optimizationproximal splitting methodsparse regularization |
| spellingShingle | Takayuki Sasaki Kazuya Hayase Masaki Kitahara Shunsuke Ono Sparse Regularization With Reverse Sorted Sum of Squares via an Unrolled Difference-of-Convex Approach IEEE Open Journal of Signal Processing Deep unrolling difference-of-convex inverse problem non-convex optimization proximal splitting method sparse regularization |
| title | Sparse Regularization With Reverse Sorted Sum of Squares via an Unrolled Difference-of-Convex Approach |
| title_full | Sparse Regularization With Reverse Sorted Sum of Squares via an Unrolled Difference-of-Convex Approach |
| title_fullStr | Sparse Regularization With Reverse Sorted Sum of Squares via an Unrolled Difference-of-Convex Approach |
| title_full_unstemmed | Sparse Regularization With Reverse Sorted Sum of Squares via an Unrolled Difference-of-Convex Approach |
| title_short | Sparse Regularization With Reverse Sorted Sum of Squares via an Unrolled Difference-of-Convex Approach |
| title_sort | sparse regularization with reverse sorted sum of squares via an unrolled difference of convex approach |
| topic | Deep unrolling difference-of-convex inverse problem non-convex optimization proximal splitting method sparse regularization |
| url | https://ieeexplore.ieee.org/document/10840312/ |
| work_keys_str_mv | AT takayukisasaki sparseregularizationwithreversesortedsumofsquaresviaanunrolleddifferenceofconvexapproach AT kazuyahayase sparseregularizationwithreversesortedsumofsquaresviaanunrolleddifferenceofconvexapproach AT masakikitahara sparseregularizationwithreversesortedsumofsquaresviaanunrolleddifferenceofconvexapproach AT shunsukeono sparseregularizationwithreversesortedsumofsquaresviaanunrolleddifferenceofconvexapproach |