Exact Support Recovery for Sparse Spikes Deconvolution

• Published in: Foundations of computational mathematics Vol. 15; no. 5; pp. 1315 - 1355
• Main Authors: Duval, Vincent, Peyré, Gabriel
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.10.2015; Springer; Springer Verlag
• Subjects: Analysis; Applications of Mathematics; Computer Science; Data Structures and Algorithms; Dirac equation; Economics; Engineering Sciences; Image processing; Information Theory; Linear and Multilinear Algebras; Math Applications in Computer Science; Mathematics; Mathematics and Statistics; Matrix Theory; Methods; Numerical Analysis; Optimization and Control; Signal and Image processing; United States; Super-resolution; Deconvolution; Sparsity; minimization; 49K40; Total variation of measures; 65J20; 46E27; inverse problem; sparsity; dual certificates

This paper studies sparse spikes deconvolution over the space of measures. We focus on the recovery properties of the support of the measure (i.e., the location of the Dirac masses) using total variation of measures (TV) regularization. This regularization is the natural extension of the ℓ 1 norm of...