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Storath, M.* ; Weinmann, A. ; Demaret, L.

Jump-sparse and sparse recovery using potts functionals.

IEEE Trans. Signal Process. 62, 3654-3666 (2014)
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We recover jump-sparse and sparse signals from blurred incomplete data corrupted by (possibly non-Gaussian) noise using inverse Potts energy functionals. We obtain analytical results (existence of minimizers, complexity) on inverse Potts functionals and provide relations to sparsity problems. We then propose a new optimization method for these functionals which is based on dynamic programming and the alternating direction method of multipliers (ADMM). A series of experiments shows that the proposed method yields very satisfactory jump-sparse and sparse reconstructions, respectively. We highlight the capability of the method by comparing it with classical and recent approaches such as TV minimization (jump-sparse signals), orthogonal matching pursuit, iterative hard thresholding, and iteratively reweighted ℓ1 minimization (sparse signals).
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Publication type Article: Journal article
Document type Scientific Article
Keywords Admm ; Deconvolution ; Denoising ; Incomplete Data ; Inverse Potts Functional ; Jump-sparsity ; Piecewise Constant Signal ; Segmentation ; Sparsity; Total Variation Minimization; Signal Reconstruction; Image-reconstruction; Energy Minimization; Graph Cuts; Algorithms; Approximations; Segmentation; Systems; Mumford
ISSN (print) / ISBN 1053-587X
e-ISSN 1941-0476
Quellenangaben Volume: 62, Issue: 14, Pages: 3654-3666 Article Number: , Supplement: ,
Publisher Institute of Electrical and Electronics Engineers (IEEE)
Publishing Place Piscataway
Reviewing status Peer reviewed