Jump-Sparse and Sparse Recovery Using Potts Functionals

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 l(1) minimization (sparse signals).


Published in:
Ieee Transactions On Signal Processing, 62, 14, 3654-3666
Year:
2014
Publisher:
Piscataway, Ieee-Inst Electrical Electronics Engineers Inc
ISSN:
1053-587X
Keywords:
Laboratories:




 Record created 2014-08-29, last modified 2018-09-13

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