Sparsest solutions of underdetermined linear systems via -minimization for |
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Authors: | Simon Foucart Ming-Jun Lai |
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Institution: | aDepartment of Mathematics, Vanderbilt University, Nashville, TN 37240, USA;bDepartment of Mathematics, University of Georgia, Athens, GA 30602, USA |
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Abstract: | We present a condition on the matrix of an underdetermined linear system which guarantees that the solution of the system with minimal ℓq-quasinorm is also the sparsest one. This generalizes, and slightly improves, a similar result for the ℓ1-norm. We then introduce a simple numerical scheme to compute solutions with minimal ℓq-quasinorm, and we study its convergence. Finally, we display the results of some experiments which indicate that the ℓq-method performs better than other available methods. |
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