# An Iterative Thresholding Algorithm for Linear Inverse Problems with a Sparsity Constraint

@article{Daubechies2003AnIT, title={An Iterative Thresholding Algorithm for Linear Inverse Problems with a Sparsity Constraint}, author={I. Daubechies and M. Defrise and C. D. Mol}, journal={Communications on Pure and Applied Mathematics}, year={2003}, volume={57}, pages={1413-1457} }

We consider linear inverse problems where the solution is assumed to have a sparse expansion on an arbitrary preassigned orthonormal basis. We prove that replacing the usual quadratic regularizing penalties by weighted p-penalties on the coefficients of such expansions, with 1 ≤ p ≤ 2, still regularizes the problem. Use of such p-penalized problems with p < 2 is often advocated when one expects the underlying ideal noiseless solution to have a sparse expansion with respect to the basis under… Expand

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