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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 minimization
(sparse signals)
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