Recovering an infinite dimensional parameter from incomplete and noisy observations is a fundamental task in many branches of mathematical and engineering science. Reasonable solution approaches require the use of regularization techniques, which incorporate a-priori knowledge about the desired unknown. For that purpose a frequently used property is the (block) sparsity of the coefficients with respect to some sparsifying transformation. In this paper we review regularization methods for sparse inverse problems and derive linear stability estimates for block-sparse analysis regularization implemented via ℓ2,1-minimization.
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