Journal
SIAM JOURNAL ON IMAGING SCIENCES
Volume 9, Issue 4, Pages 1756-1787Publisher
SIAM PUBLICATIONS
DOI: 10.1137/16M1064064
Keywords
alternating minimization; blind image deconvolution; block coordinate descent; heavy ball method; Kurdyka-Lojasiewicz property; nonconvex and nonsmooth minimization; sparse nonnegative matrix factorization; dictionary learning
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Funding
- Austrian science fund (FWF) under the project EANOI [11148]
- ERC starting grant HOMOVIS [640156]
- Austrian Science Fund (FWF) [I1148] Funding Source: Austrian Science Fund (FWF)
- Austrian Science Fund (FWF) [I 1148] Funding Source: researchfish
- European Research Council (ERC) [640156] Funding Source: European Research Council (ERC)
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In this paper we study nonconvex and nonsmooth optimization problems with semialgebraic data, where the variables vector is split into several blocks of variables. The problem consists of one smooth function of the entire variables vector and the sum of nonsmooth functions for each block separately. We analyze an inertial version of the proximal alternating linearized minimization algorithm and prove its global convergence to a critical point of the objective function at hand. We illustrate our theoretical findings by presenting numerical experiments on blind image deconvolution, on sparse nonnegative matrix factorization and on dictionary learning, which demonstrate the viability and effectiveness of the proposed method.
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