Abstract
We present a condition on the matrix of an underdetermined linear system which guarantees that the solution of the system with minimal ℓ q -quasinorm is also the sparsest one. This generalizes, and slightly improves, a similar result for the ℓ 1 -norm. We then introduce a simple numerical scheme to compute solutions with minimal ℓ q -quasinorm, and we study its convergence. Finally, we display the results of some experiments which indicate that the ℓ q -method performs better than other available methods.
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