Journal
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
Volume 25, Issue 2, Pages 187-208Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.acha.2007.10.005
Keywords
linear inverse problems; joint sparsity; thresholded Landweber iterations; frames; variational calculus on sequence spaces; Gamma-convergence
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This article provides a variational formulation for hard and firm thresholding. A related functional can be used to regularize inverse problems by sparsity constraints. We show that a damped hard or firm thresholded Landweber iteration converges to its minimizer. This provides an alternative to an algorithm recently studied by the authors. We prove stability of minimizers with respect to the parameters of the functional by means of Gamma-convergence. All investigations are done in the general setting of vector-valued (multi-channel) data. (c) 2007 Elsevier Inc. All rights reserved.
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