Inexact Fixed-Point Proximity Algorithm for the ℓ0 Sparse Regularization Problem
We study inexact fixed-point proximity algorithms for solving a class of sparse regularization problems involving the ℓ 0 norm. Specifically, the ℓ 0 model has an objective function that is the sum of a convex fidelity term and a Moreau envelope of the ℓ 0 norm regularization term. Such an ℓ 0 model...
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| Veröffentlicht in: | Journal of scientific computing Jg. 100; H. 2; S. 58 |
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01.08.2024
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| Abstract | We study
inexact
fixed-point proximity algorithms for solving a class of sparse regularization problems involving the
ℓ
0
norm. Specifically, the
ℓ
0
model has an objective function that is the sum of a convex fidelity term and a Moreau envelope of the
ℓ
0
norm regularization term. Such an
ℓ
0
model is non-convex. Existing exact algorithms for solving the problems require the availability of closed-form formulas for the proximity operator of convex functions involved in the objective function. When such formulas are not available, numerical computation of the proximity operator becomes inevitable. This leads to inexact iteration algorithms. We investigate in this paper how the numerical error for every step of the iteration should be controlled to ensure global convergence of the inexact algorithms. We establish a theoretical result that guarantees the sequence generated by the proposed inexact algorithm converges to a local minimizer of the optimization problem. We implement the proposed algorithms for three applications of practical importance in machine learning and image science, which include regression, classification, and image deblurring. The numerical results demonstrate the convergence of the proposed algorithm and confirm that local minimizers of the
ℓ
0
models found by the proposed inexact algorithm outperform global minimizers of the corresponding
ℓ
1
models, in terms of approximation accuracy and sparsity of the solutions. |
|---|---|
| AbstractList | We study inexact fixed-point proximity algorithms for solving a class of sparse regularization problems involving the ℓ0 norm. Specifically, the ℓ0 model has an objective function that is the sum of a convex fidelity term and a Moreau envelope of the ℓ0 norm regularization term. Such an ℓ0 model is non-convex. Existing exact algorithms for solving the problems require the availability of closed-form formulas for the proximity operator of convex functions involved in the objective function. When such formulas are not available, numerical computation of the proximity operator becomes inevitable. This leads to inexact iteration algorithms. We investigate in this paper how the numerical error for every step of the iteration should be controlled to ensure global convergence of the inexact algorithms. We establish a theoretical result that guarantees the sequence generated by the proposed inexact algorithm converges to a local minimizer of the optimization problem. We implement the proposed algorithms for three applications of practical importance in machine learning and image science, which include regression, classification, and image deblurring. The numerical results demonstrate the convergence of the proposed algorithm and confirm that local minimizers of the ℓ0 models found by the proposed inexact algorithm outperform global minimizers of the corresponding ℓ1 models, in terms of approximation accuracy and sparsity of the solutions. We study inexact fixed-point proximity algorithms for solving a class of sparse regularization problems involving the ℓ 0 norm. Specifically, the ℓ 0 model has an objective function that is the sum of a convex fidelity term and a Moreau envelope of the ℓ 0 norm regularization term. Such an ℓ 0 model is non-convex. Existing exact algorithms for solving the problems require the availability of closed-form formulas for the proximity operator of convex functions involved in the objective function. When such formulas are not available, numerical computation of the proximity operator becomes inevitable. This leads to inexact iteration algorithms. We investigate in this paper how the numerical error for every step of the iteration should be controlled to ensure global convergence of the inexact algorithms. We establish a theoretical result that guarantees the sequence generated by the proposed inexact algorithm converges to a local minimizer of the optimization problem. We implement the proposed algorithms for three applications of practical importance in machine learning and image science, which include regression, classification, and image deblurring. The numerical results demonstrate the convergence of the proposed algorithm and confirm that local minimizers of the ℓ 0 models found by the proposed inexact algorithm outperform global minimizers of the corresponding ℓ 1 models, in terms of approximation accuracy and sparsity of the solutions. |
| Author | Xu, Yuesheng Fang, Ronglong Yan, Mingsong |
| Author_xml | – sequence: 1 givenname: Ronglong surname: Fang fullname: Fang, Ronglong organization: Department of Mathematics and Statistics, Old Dominion University – sequence: 2 givenname: Yuesheng surname: Xu fullname: Xu, Yuesheng email: y1xu@odu.edu organization: Department of Mathematics and Statistics, Old Dominion University – sequence: 3 givenname: Mingsong surname: Yan fullname: Yan, Mingsong organization: Department of Mathematics and Statistics, Old Dominion University |
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| Cites_doi | 10.1561/2200000016 10.1109/TSP.2014.2304932 10.1088/1361-6420/ab23da 10.1088/0266-5611/27/4/045009 10.1109/TIT.2006.885507 10.1137/1.9780898718874 10.1137/110844805 10.1007/s10915-019-01045-7 10.1080/00036811.2010.490524 10.1142/S0219530522500105 10.1090/S0002-9904-1943-07818-4 10.1198/016214506000000735 10.1023/A:1008777829180 10.1007/s10107-011-0484-9 10.1007/s10107-015-0964-4 10.1006/jfan.1996.3079 10.1016/j.acha.2015.03.001 10.1145/1961189.1961199 10.1137/0314056 10.1137/1.9781611970104 10.1007/s10851-010-0251-1 10.1007/s10915-018-0757-z 10.1109/TIP.2013.2271852 10.1137/S0097539792240406 10.1198/016214501753382273 10.1109/TIT.2005.858979 10.1109/TIT.2006.871582 10.1007/978-1-4419-9467-7 10.1016/j.acha.2004.02.003 10.1016/j.acha.2012.03.009 10.1016/j.apnum.2023.02.011 10.1007/s10915-022-01906-8 10.1137/1.9781611974997 10.1016/j.acha.2013.11.002 10.1007/s10444-014-9363-2 10.1137/080724265 10.1137/S0036144598336745 10.1016/0898-1221(76)90003-1 |
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| Keywords | The 68U10 Inexact fixed-point proximity algorithm Non-convex optimization 65K10 Sparse regularization 90C26 norm |
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| References | Mallat (CR31) 1999 Daubechies (CR13) 1992 CR34 Courant (CR12) 1943; 49 Chang, Lin (CR10) 2011; 2 Donoho (CR14) 2006; 52 Candes, Tao (CR7) 2006; 52 Liang, Fadili, Peyré (CR29) 2016; 159 Villa, Salzo, Baldassarre, Verri (CR44) 2013; 23 Gabay, Mercier (CR17) 1976; 2 Zheng, Li, Krol, Schmidtlein, Zeng, Xu (CR52) 2019; 35 CR4 Zou (CR53) 2006; 101 Hansen, Nagy, O’leary (CR20) 2006 Natarajan (CR33) 1995; 24 Boyd, Parikh, Chu, Peleato, Eckstein (CR5) 2011; 3 Li, Song, Xu (CR26) 2019; 81 Ron, Shen (CR36) 1997; 148 Lojasiewicz (CR30) 1963; 117 Chan, Riemenschneider, Shen, Shen (CR9) 2004; 17 CR47 Suter (CR42) 1998 Tan, Eldar, Beck, Nehorai (CR43) 2014; 62 Li, Shen, Xu, Zhang (CR24) 2015; 41 Wu, Xu (CR48) 2022; 92 Shen, Xu, Zhang (CR38) 2014; 37 Chambolle, Pock (CR8) 2011; 40 Li, Song, Xu (CR25) 2018; 15 CR19 CR18 CR15 Attouch, Bolte, Svaiter (CR1) 2013; 137 CR11 CR51 Fan, Li (CR16) 2001; 96 Strang (CR41) 1999; 41 Bauschke, Combettes (CR2) 2011 Candes, Tao (CR6) 2005; 51 Micchelli, Shen, Xu (CR32) 2011; 27 Rockafellar (CR35) 1976; 14 Xu (CR49) 2023; 187 Xu (CR50) 2023; 21 Lefkimmiatis, Unser (CR23) 2013; 22 Wang, Yin, Zeng (CR46) 2019; 78 Wang, Yang, Yin, Zhang (CR45) 2008; 1 Beck (CR3) 2017 Lian, Shen, Xu, Yang (CR28) 2011; 90 CR27 CR22 CR21 Shen, Xu, Zeng (CR37) 2016; 41 Solodov, Svaiter (CR39) 1999; 7 Song, Zhang, Hickernell (CR40) 2013; 34 |
| References_xml | – ident: CR22 – volume: 3 start-page: 1 issue: 1 year: 2011 end-page: 122 ident: CR5 article-title: Distributed optimization and statistical learning via the alternating direction method of multipliers publication-title: Found. Trends Mach. Learn. doi: 10.1561/2200000016 – volume: 62 start-page: 1762 issue: 7 year: 2014 end-page: 1774 ident: CR43 article-title: Smoothing and decomposition for analysis sparse recovery publication-title: IEEE Trans. Signal Process. doi: 10.1109/TSP.2014.2304932 – volume: 35 issue: 11 year: 2019 ident: CR52 article-title: Sparsity promoting regularization for effective noise suppression in SPECT image reconstruction publication-title: Inverse Probl. doi: 10.1088/1361-6420/ab23da – ident: CR4 – ident: CR51 – volume: 27 year: 2011 ident: CR32 article-title: Proximity algorithms for image models: denoising publication-title: Inverse Probl. doi: 10.1088/0266-5611/27/4/045009 – volume: 52 start-page: 5406 year: 2006 end-page: 5425 ident: CR7 article-title: Near-optimal signal recovery from random projections: Universal encoding strategies? publication-title: IEEE Trans. Inf. doi: 10.1109/TIT.2006.885507 – year: 2006 ident: CR20 publication-title: Deblurring Images: Matrices, Spectra, and Filtering doi: 10.1137/1.9780898718874 – volume: 23 start-page: 1607 year: 2013 end-page: 1633 ident: CR44 article-title: Accelerated and inexact forward–backward algorithms publication-title: SIAM J. Optim. doi: 10.1137/110844805 – volume: 81 start-page: 923 year: 2019 end-page: 940 ident: CR26 article-title: A two-step fixed-point proximity algorithm for a class of non-differentiable optimization models in machine learning publication-title: J. Sci. Comput. doi: 10.1007/s10915-019-01045-7 – volume: 90 start-page: 1299 year: 2011 end-page: 1322 ident: CR28 article-title: Filters of wavelets on invariant sets for image denoising publication-title: Appl. Anal. doi: 10.1080/00036811.2010.490524 – volume: 21 start-page: 901 year: 2023 end-page: 929 ident: CR50 article-title: Sparse regularization with the norm publication-title: Anal. Appl. doi: 10.1142/S0219530522500105 – volume: 49 start-page: 1 year: 1943 end-page: 23 ident: CR12 article-title: Variational methods for the solution of problems of equilibrium and vibrations publication-title: Bull. Am. Math. doi: 10.1090/S0002-9904-1943-07818-4 – volume: 101 start-page: 1418 year: 2006 end-page: 1429 ident: CR53 article-title: The adaptive lasso and its oracle properties publication-title: J. Am. Stat. Assoc. doi: 10.1198/016214506000000735 – ident: CR21 – volume: 7 start-page: 323 year: 1999 end-page: 345 ident: CR39 article-title: A hybrid approximate extragradient-proximal point algorithm using the enlargement of a maximal monotone operator publication-title: Set-Valued Anal. doi: 10.1023/A:1008777829180 – volume: 137 start-page: 91 year: 2013 end-page: 129 ident: CR1 article-title: Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward–backward splitting, and regularized Gauss–Seidel methods publication-title: Math. Program. doi: 10.1007/s10107-011-0484-9 – ident: CR19 – volume: 159 start-page: 403 year: 2016 end-page: 434 ident: CR29 article-title: Convergence rates with inexact non-expansive operators publication-title: Math. Program. doi: 10.1007/s10107-015-0964-4 – ident: CR15 – volume: 148 start-page: 408 year: 1997 end-page: 447 ident: CR36 article-title: Affine systems in : the analysis of the analysis operator publication-title: J. Funct. Anal. doi: 10.1006/jfan.1996.3079 – volume: 41 start-page: 26 year: 2016 end-page: 53 ident: CR37 article-title: Wavelet inpainting with the sparse regularization publication-title: Appl. Comput. Harmon. Anal. doi: 10.1016/j.acha.2015.03.001 – ident: CR11 – volume: 2 start-page: 1 year: 2011 end-page: 27 ident: CR10 article-title: LIBSVM: a library for support vector machines publication-title: ACM Trans. Intell. doi: 10.1145/1961189.1961199 – volume: 14 start-page: 877 year: 1976 end-page: 898 ident: CR35 article-title: Monotone operators and the proximal point algorithm publication-title: SIAM J. Control. Optim. doi: 10.1137/0314056 – year: 1992 ident: CR13 publication-title: Ten Lectures on Wavelets doi: 10.1137/1.9781611970104 – volume: 40 start-page: 120 year: 2011 end-page: 145 ident: CR8 article-title: A first-order primal–dual algorithm for convex problems with applications to imaging publication-title: J. Math. Imaging Vis. doi: 10.1007/s10851-010-0251-1 – volume: 78 start-page: 29 year: 2019 end-page: 63 ident: CR46 article-title: Global convergence of ADMM in nonconvex non-smooth optimization publication-title: J. Sci. Comput. doi: 10.1007/s10915-018-0757-z – volume: 22 start-page: 4314 issue: 11 year: 2013 end-page: 4327 ident: CR23 article-title: Poisson image reconstruction with Hessian Schatten-norm regularization publication-title: IEEE Trans. Image Process. doi: 10.1109/TIP.2013.2271852 – ident: CR18 – ident: CR47 – volume: 24 start-page: 227 year: 1995 end-page: 234 ident: CR33 article-title: Sparse approximate solutions to linear systems publication-title: SIAM J. Comput. doi: 10.1137/S0097539792240406 – year: 1998 ident: CR42 publication-title: Multirate and Wavelet Signal Processing – volume: 96 start-page: 1348 year: 2001 end-page: 1360 ident: CR16 article-title: Variable selection via nonconcave penalized likelihood and its oracle properties publication-title: J. Am. Stat. Assoc. doi: 10.1198/016214501753382273 – volume: 51 start-page: 4203 year: 2005 end-page: 4215 ident: CR6 article-title: Decoding by linear programming publication-title: IEEE Trans. Inf. doi: 10.1109/TIT.2005.858979 – volume: 52 start-page: 1289 year: 2006 end-page: 1306 ident: CR14 article-title: Compressed sensing publication-title: IEEE Trans. Inf. doi: 10.1109/TIT.2006.871582 – year: 2011 ident: CR2 publication-title: Convex Analysis and Monotone Operator Theory in Hilbert Spaces doi: 10.1007/978-1-4419-9467-7 – volume: 17 start-page: 91 year: 2004 end-page: 115 ident: CR9 article-title: Tight frame: an efficient way for high-resolution image reconstruction publication-title: Appl. Comput. Harmon. Anal. doi: 10.1016/j.acha.2004.02.003 – volume: 34 start-page: 96 year: 2013 end-page: 116 ident: CR40 article-title: Reproducing kernel Banach spaces with the norm publication-title: Appl. Comput. Harmon. Anal. doi: 10.1016/j.acha.2012.03.009 – volume: 187 start-page: 138 year: 2023 end-page: 157 ident: CR49 article-title: Sparse machine learning in Banach spaces publication-title: Appl. Numer. Math. doi: 10.1016/j.apnum.2023.02.011 – ident: CR27 – volume: 15 start-page: 154 year: 2018 end-page: 169 ident: CR25 article-title: A fixed-point proximity approach to solving the support vector regression with the group lasso regularization publication-title: Int. J. Numer. Anal. Model. – volume: 92 start-page: 1 year: 2022 end-page: 35 ident: CR48 article-title: Inverting incomplete Fourier transforms by a sparse regularization model and applications in seismic wavefield modeling publication-title: J. Sci. Comput. doi: 10.1007/s10915-022-01906-8 – year: 2017 ident: CR3 publication-title: First-Order Methods in Optimization doi: 10.1137/1.9781611974997 – year: 1999 ident: CR31 publication-title: A Wavelet Tour of Signal Processing – volume: 117 start-page: 87 year: 1963 end-page: 89 ident: CR30 article-title: Une propriété topologique des sous-ensembles analytiques réels publication-title: Les équations aux dérivées partielles – ident: CR34 – volume: 37 start-page: 171 issue: 1 year: 2014 end-page: 184 ident: CR38 article-title: An approximate sparsity model for inpainting publication-title: Appl. Comput. Harmon. Anal. doi: 10.1016/j.acha.2013.11.002 – volume: 41 start-page: 387 year: 2015 end-page: 422 ident: CR24 article-title: Multi-step fixed-point proximity algorithms for solving a class of optimization problems arising from image processing publication-title: Adv. Comput. Math. doi: 10.1007/s10444-014-9363-2 – volume: 1 start-page: 248 issue: 3 year: 2008 end-page: 272 ident: CR45 article-title: A new alternating minimization algorithm for total variation image reconstruction publication-title: SIAM J. Imaging Sci. doi: 10.1137/080724265 – volume: 41 start-page: 135 year: 1999 end-page: 147 ident: CR41 article-title: The discrete cosine transform publication-title: SIAM Rev. doi: 10.1137/S0036144598336745 – volume: 2 start-page: 17 issue: 1 year: 1976 end-page: 40 ident: CR17 article-title: A dual algorithm for the solution of nonlinear variational problems via finite element approximation publication-title: Comput. Math. Appl. doi: 10.1016/0898-1221(76)90003-1 |
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| Snippet | We study
inexact
fixed-point proximity algorithms for solving a class of sparse regularization problems involving the
ℓ
0
norm. Specifically, the
ℓ
0
model has... We study inexact fixed-point proximity algorithms for solving a class of sparse regularization problems involving the ℓ0 norm. Specifically, the ℓ0 model has... |
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| SubjectTerms | Algorithms Availability Computational Mathematics and Numerical Analysis Convergence Convex analysis Fixed points (mathematics) Image classification Iterative algorithms Machine learning Mathematical analysis Mathematical and Computational Engineering Mathematical and Computational Physics Mathematics Mathematics and Statistics Numerical analysis Operators (mathematics) Optimization Proximity Regularization Sparsity Theoretical Wavelet transforms |
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| Title | Inexact Fixed-Point Proximity Algorithm for the ℓ0 Sparse Regularization Problem |
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| Volume | 100 |
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