A modified non-convex Cauchy total variation regularization model for image restoration
Abstract This study introduces a modified non-convex Cauchy total variation (MCauchyTV) model based on the prior property of image. First, we improve the probability density function of the Cauchy distribution, and propose a general Cauchy penalty function. Then, its proximity operator is derived an...
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| Autor*in: |
Lu, Yi [verfasserIn] Wu, Xiru [verfasserIn] Zhang, Benxin [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2024 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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| Übergeordnetes Werk: |
Enthalten in: Computational and applied mathematics - Springer International Publishing, 2003, 44(2024), 1 vom: 23. Okt. |
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| Übergeordnetes Werk: |
volume:44 ; year:2024 ; number:1 ; day:23 ; month:10 |
| Links: |
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| DOI / URN: |
10.1007/s40314-024-02959-1 |
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SPR05797005X |
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| 520 | |a Abstract This study introduces a modified non-convex Cauchy total variation (MCauchyTV) model based on the prior property of image. First, we improve the probability density function of the Cauchy distribution, and propose a general Cauchy penalty function. Then, its proximity operator is derived and has a closed-form solution. Second, a non-convex MCauchyTV model is implemented with the proposed multivariate Cauchy function. Following, the model is solved by an effective alternating direction method of multipliers. Its subproblems can be solved quickly using the fast Fourier transform and the proximity operator. Third, we analyze and prove the conditions under which the MCauchyTV proximity operator preserves convexity, ensuring the exact tuning of the system parameters and the convergence of the ADMM. Finally, the efficiency and viability of the MCauchyTV model are validated by image deblurring and magnetic resonance imaging reconstruction. | ||
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| 650 | 4 | |a Image deblurring |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Magnetic resonance imaging reconstruction |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Wu, Xiru |e verfasserin |4 aut | |
| 700 | 1 | |a Zhang, Benxin |e verfasserin |4 aut | |
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10.1007/s40314-024-02959-1 doi (DE-627)SPR05797005X (SPR)s40314-024-02959-1-e DE-627 ger DE-627 rakwb eng 510 VZ 31.76 bkl 31.80 bkl Lu, Yi verfasserin aut A modified non-convex Cauchy total variation regularization model for image restoration 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract This study introduces a modified non-convex Cauchy total variation (MCauchyTV) model based on the prior property of image. First, we improve the probability density function of the Cauchy distribution, and propose a general Cauchy penalty function. Then, its proximity operator is derived and has a closed-form solution. Second, a non-convex MCauchyTV model is implemented with the proposed multivariate Cauchy function. Following, the model is solved by an effective alternating direction method of multipliers. Its subproblems can be solved quickly using the fast Fourier transform and the proximity operator. Third, we analyze and prove the conditions under which the MCauchyTV proximity operator preserves convexity, ensuring the exact tuning of the system parameters and the convergence of the ADMM. Finally, the efficiency and viability of the MCauchyTV model are validated by image deblurring and magnetic resonance imaging reconstruction. Modified Cauchy total variation (dpeaa)DE-He213 Proximal operator (dpeaa)DE-He213 ADMM (dpeaa)DE-He213 Image deblurring (dpeaa)DE-He213 Magnetic resonance imaging reconstruction (dpeaa)DE-He213 Wu, Xiru verfasserin aut Zhang, Benxin verfasserin aut Enthalten in Computational and applied mathematics Springer International Publishing, 2003 44(2024), 1 vom: 23. Okt. (DE-627)47617502X (DE-600)2171678-X 1807-0302 nnns volume:44 year:2024 number:1 day:23 month:10 https://dx.doi.org/10.1007/s40314-024-02959-1 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_72 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2574 GBV_ILN_4029 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4116 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4155 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4318 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4598 GBV_ILN_4700 31.76 VZ 31.80 VZ AR 44 2024 1 23 10 |
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10.1007/s40314-024-02959-1 doi (DE-627)SPR05797005X (SPR)s40314-024-02959-1-e DE-627 ger DE-627 rakwb eng 510 VZ 31.76 bkl 31.80 bkl Lu, Yi verfasserin aut A modified non-convex Cauchy total variation regularization model for image restoration 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract This study introduces a modified non-convex Cauchy total variation (MCauchyTV) model based on the prior property of image. First, we improve the probability density function of the Cauchy distribution, and propose a general Cauchy penalty function. Then, its proximity operator is derived and has a closed-form solution. Second, a non-convex MCauchyTV model is implemented with the proposed multivariate Cauchy function. Following, the model is solved by an effective alternating direction method of multipliers. Its subproblems can be solved quickly using the fast Fourier transform and the proximity operator. Third, we analyze and prove the conditions under which the MCauchyTV proximity operator preserves convexity, ensuring the exact tuning of the system parameters and the convergence of the ADMM. Finally, the efficiency and viability of the MCauchyTV model are validated by image deblurring and magnetic resonance imaging reconstruction. Modified Cauchy total variation (dpeaa)DE-He213 Proximal operator (dpeaa)DE-He213 ADMM (dpeaa)DE-He213 Image deblurring (dpeaa)DE-He213 Magnetic resonance imaging reconstruction (dpeaa)DE-He213 Wu, Xiru verfasserin aut Zhang, Benxin verfasserin aut Enthalten in Computational and applied mathematics Springer International Publishing, 2003 44(2024), 1 vom: 23. Okt. (DE-627)47617502X (DE-600)2171678-X 1807-0302 nnns volume:44 year:2024 number:1 day:23 month:10 https://dx.doi.org/10.1007/s40314-024-02959-1 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_72 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2574 GBV_ILN_4029 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4116 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4155 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4318 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4598 GBV_ILN_4700 31.76 VZ 31.80 VZ AR 44 2024 1 23 10 |
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10.1007/s40314-024-02959-1 doi (DE-627)SPR05797005X (SPR)s40314-024-02959-1-e DE-627 ger DE-627 rakwb eng 510 VZ 31.76 bkl 31.80 bkl Lu, Yi verfasserin aut A modified non-convex Cauchy total variation regularization model for image restoration 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract This study introduces a modified non-convex Cauchy total variation (MCauchyTV) model based on the prior property of image. First, we improve the probability density function of the Cauchy distribution, and propose a general Cauchy penalty function. Then, its proximity operator is derived and has a closed-form solution. Second, a non-convex MCauchyTV model is implemented with the proposed multivariate Cauchy function. Following, the model is solved by an effective alternating direction method of multipliers. Its subproblems can be solved quickly using the fast Fourier transform and the proximity operator. Third, we analyze and prove the conditions under which the MCauchyTV proximity operator preserves convexity, ensuring the exact tuning of the system parameters and the convergence of the ADMM. Finally, the efficiency and viability of the MCauchyTV model are validated by image deblurring and magnetic resonance imaging reconstruction. Modified Cauchy total variation (dpeaa)DE-He213 Proximal operator (dpeaa)DE-He213 ADMM (dpeaa)DE-He213 Image deblurring (dpeaa)DE-He213 Magnetic resonance imaging reconstruction (dpeaa)DE-He213 Wu, Xiru verfasserin aut Zhang, Benxin verfasserin aut Enthalten in Computational and applied mathematics Springer International Publishing, 2003 44(2024), 1 vom: 23. Okt. (DE-627)47617502X (DE-600)2171678-X 1807-0302 nnns volume:44 year:2024 number:1 day:23 month:10 https://dx.doi.org/10.1007/s40314-024-02959-1 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_72 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2574 GBV_ILN_4029 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4116 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4155 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4318 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4598 GBV_ILN_4700 31.76 VZ 31.80 VZ AR 44 2024 1 23 10 |
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10.1007/s40314-024-02959-1 doi (DE-627)SPR05797005X (SPR)s40314-024-02959-1-e DE-627 ger DE-627 rakwb eng 510 VZ 31.76 bkl 31.80 bkl Lu, Yi verfasserin aut A modified non-convex Cauchy total variation regularization model for image restoration 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract This study introduces a modified non-convex Cauchy total variation (MCauchyTV) model based on the prior property of image. First, we improve the probability density function of the Cauchy distribution, and propose a general Cauchy penalty function. Then, its proximity operator is derived and has a closed-form solution. Second, a non-convex MCauchyTV model is implemented with the proposed multivariate Cauchy function. Following, the model is solved by an effective alternating direction method of multipliers. Its subproblems can be solved quickly using the fast Fourier transform and the proximity operator. Third, we analyze and prove the conditions under which the MCauchyTV proximity operator preserves convexity, ensuring the exact tuning of the system parameters and the convergence of the ADMM. Finally, the efficiency and viability of the MCauchyTV model are validated by image deblurring and magnetic resonance imaging reconstruction. Modified Cauchy total variation (dpeaa)DE-He213 Proximal operator (dpeaa)DE-He213 ADMM (dpeaa)DE-He213 Image deblurring (dpeaa)DE-He213 Magnetic resonance imaging reconstruction (dpeaa)DE-He213 Wu, Xiru verfasserin aut Zhang, Benxin verfasserin aut Enthalten in Computational and applied mathematics Springer International Publishing, 2003 44(2024), 1 vom: 23. Okt. (DE-627)47617502X (DE-600)2171678-X 1807-0302 nnns volume:44 year:2024 number:1 day:23 month:10 https://dx.doi.org/10.1007/s40314-024-02959-1 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_72 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2574 GBV_ILN_4029 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4116 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4155 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4318 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4598 GBV_ILN_4700 31.76 VZ 31.80 VZ AR 44 2024 1 23 10 |
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10.1007/s40314-024-02959-1 doi (DE-627)SPR05797005X (SPR)s40314-024-02959-1-e DE-627 ger DE-627 rakwb eng 510 VZ 31.76 bkl 31.80 bkl Lu, Yi verfasserin aut A modified non-convex Cauchy total variation regularization model for image restoration 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract This study introduces a modified non-convex Cauchy total variation (MCauchyTV) model based on the prior property of image. First, we improve the probability density function of the Cauchy distribution, and propose a general Cauchy penalty function. Then, its proximity operator is derived and has a closed-form solution. Second, a non-convex MCauchyTV model is implemented with the proposed multivariate Cauchy function. Following, the model is solved by an effective alternating direction method of multipliers. Its subproblems can be solved quickly using the fast Fourier transform and the proximity operator. Third, we analyze and prove the conditions under which the MCauchyTV proximity operator preserves convexity, ensuring the exact tuning of the system parameters and the convergence of the ADMM. Finally, the efficiency and viability of the MCauchyTV model are validated by image deblurring and magnetic resonance imaging reconstruction. Modified Cauchy total variation (dpeaa)DE-He213 Proximal operator (dpeaa)DE-He213 ADMM (dpeaa)DE-He213 Image deblurring (dpeaa)DE-He213 Magnetic resonance imaging reconstruction (dpeaa)DE-He213 Wu, Xiru verfasserin aut Zhang, Benxin verfasserin aut Enthalten in Computational and applied mathematics Springer International Publishing, 2003 44(2024), 1 vom: 23. Okt. (DE-627)47617502X (DE-600)2171678-X 1807-0302 nnns volume:44 year:2024 number:1 day:23 month:10 https://dx.doi.org/10.1007/s40314-024-02959-1 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_72 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2574 GBV_ILN_4029 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4116 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4155 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4318 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4598 GBV_ILN_4700 31.76 VZ 31.80 VZ AR 44 2024 1 23 10 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">SPR05797005X</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20241023064743.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">241023s2024 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s40314-024-02959-1</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR05797005X</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s40314-024-02959-1-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">31.76</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">31.80</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Lu, Yi</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">A modified non-convex Cauchy total variation regularization model for image restoration</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2024</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract This study introduces a modified non-convex Cauchy total variation (MCauchyTV) model based on the prior property of image. First, we improve the probability density function of the Cauchy distribution, and propose a general Cauchy penalty function. Then, its proximity operator is derived and has a closed-form solution. Second, a non-convex MCauchyTV model is implemented with the proposed multivariate Cauchy function. Following, the model is solved by an effective alternating direction method of multipliers. Its subproblems can be solved quickly using the fast Fourier transform and the proximity operator. Third, we analyze and prove the conditions under which the MCauchyTV proximity operator preserves convexity, ensuring the exact tuning of the system parameters and the convergence of the ADMM. Finally, the efficiency and viability of the MCauchyTV model are validated by image deblurring and magnetic resonance imaging reconstruction.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Modified Cauchy total variation</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Proximal operator</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">ADMM</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Image deblurring</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Magnetic resonance imaging reconstruction</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Wu, Xiru</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Zhang, Benxin</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Computational and applied mathematics</subfield><subfield code="d">Springer International Publishing, 2003</subfield><subfield code="g">44(2024), 1 vom: 23. 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Lu, Yi |
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Lu, Yi ddc 510 bkl 31.76 bkl 31.80 misc Modified Cauchy total variation misc Proximal operator misc ADMM misc Image deblurring misc Magnetic resonance imaging reconstruction A modified non-convex Cauchy total variation regularization model for image restoration |
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510 VZ 31.76 bkl 31.80 bkl A modified non-convex Cauchy total variation regularization model for image restoration Modified Cauchy total variation (dpeaa)DE-He213 Proximal operator (dpeaa)DE-He213 ADMM (dpeaa)DE-He213 Image deblurring (dpeaa)DE-He213 Magnetic resonance imaging reconstruction (dpeaa)DE-He213 |
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A modified non-convex Cauchy total variation regularization model for image restoration |
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a modified non-convex cauchy total variation regularization model for image restoration |
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A modified non-convex Cauchy total variation regularization model for image restoration |
| abstract |
Abstract This study introduces a modified non-convex Cauchy total variation (MCauchyTV) model based on the prior property of image. First, we improve the probability density function of the Cauchy distribution, and propose a general Cauchy penalty function. Then, its proximity operator is derived and has a closed-form solution. Second, a non-convex MCauchyTV model is implemented with the proposed multivariate Cauchy function. Following, the model is solved by an effective alternating direction method of multipliers. Its subproblems can be solved quickly using the fast Fourier transform and the proximity operator. Third, we analyze and prove the conditions under which the MCauchyTV proximity operator preserves convexity, ensuring the exact tuning of the system parameters and the convergence of the ADMM. Finally, the efficiency and viability of the MCauchyTV model are validated by image deblurring and magnetic resonance imaging reconstruction. © The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| abstractGer |
Abstract This study introduces a modified non-convex Cauchy total variation (MCauchyTV) model based on the prior property of image. First, we improve the probability density function of the Cauchy distribution, and propose a general Cauchy penalty function. Then, its proximity operator is derived and has a closed-form solution. Second, a non-convex MCauchyTV model is implemented with the proposed multivariate Cauchy function. Following, the model is solved by an effective alternating direction method of multipliers. Its subproblems can be solved quickly using the fast Fourier transform and the proximity operator. Third, we analyze and prove the conditions under which the MCauchyTV proximity operator preserves convexity, ensuring the exact tuning of the system parameters and the convergence of the ADMM. Finally, the efficiency and viability of the MCauchyTV model are validated by image deblurring and magnetic resonance imaging reconstruction. © The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| abstract_unstemmed |
Abstract This study introduces a modified non-convex Cauchy total variation (MCauchyTV) model based on the prior property of image. First, we improve the probability density function of the Cauchy distribution, and propose a general Cauchy penalty function. Then, its proximity operator is derived and has a closed-form solution. Second, a non-convex MCauchyTV model is implemented with the proposed multivariate Cauchy function. Following, the model is solved by an effective alternating direction method of multipliers. Its subproblems can be solved quickly using the fast Fourier transform and the proximity operator. Third, we analyze and prove the conditions under which the MCauchyTV proximity operator preserves convexity, ensuring the exact tuning of the system parameters and the convergence of the ADMM. Finally, the efficiency and viability of the MCauchyTV model are validated by image deblurring and magnetic resonance imaging reconstruction. © The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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A modified non-convex Cauchy total variation regularization model for image restoration |
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Wu, Xiru Zhang, Benxin |
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|
| score |
7.400791 |