New regularization method and iteratively reweighted algorithm for sparse vector recovery |
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Authors: | Wei ZHU Hui ZHANG Lizhi CHENG |
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Institution: | 1. Post-doctoral Research Station of Statistics, School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, Hunan Province, China;2. Department of Mathematics, National University of Defense Technology, Changsha 410073, China |
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Abstract: | 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. |
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Keywords: | regularization method iteratively reweighted algorithm(IR-algorithm) sparse vector recovery |
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