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Jump-Sparse and Sparse Recovery Using Potts Functionals

M. Storath, A. Weinmann, L. Demaret

IEEE Transactions on Signal Processing, vol. 62, no. 14, pp. 3654–3666, July 15, 2014.

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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AUTHOR="Storath, M. and Weinmann, A. and Demaret, L.",
TITLE="Jump-Sparse and Sparse Recovery Using {P}otts Functionals",
JOURNAL="{IEEE} Transactions on Signal Processing",
YEAR="2014",
volume="62",
number="14",
pages="3654--3666",
month="July 15,",
note="")

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