New regularization method and iteratively reweighted algorithm for sparse vector recovery

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Motivated by the study of regularization for sparse problems, we propose a new regularization method for sparse vector recovery. We derive sufficient conditions on the well-posedness of the new regularization, and design an iterative algorithm, namely the iteratively reweighted algorithm (IR-algorithm), for efficiently computing the sparse solutions to the proposed regularization model. The convergence of the IR-algorithm and the setting of the regularization parameters are analyzed at length. Finally, we present numerical examples to illustrate the features of the new regularization and algorithm.