FA ] 2 N ov 2 00 3 An iterative thresholding algorithm for linear inverse problems with a sparsity constraint

@inproceedings{Daubechies2003FA2,
  title={FA ] 2 N ov 2 00 3 An iterative thresholding algorithm for linear inverse problems with a sparsity constraint},
  author={Ingrid Daubechies and Michel Defrise and Christine De Mol and February},
  year={2003}
}
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 ppenalties 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… CONTINUE READING
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