Math @ Duke

Publications [#287169] of Ingrid Daubechies
Papers Published
 Daubechies, I; Defrise, M; De Mol, C, An iterative thresholding algorithm for linear inverse problems with a sparsity constraint,
Communications on Pure and Applied Mathematics, vol. 57 no. 11
(November, 2004),
pp. 14131457, WILEY [doi]
(last updated on 2019/05/19)
Abstract: 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 of ℓP  penalties on the coefficients of such expansions, with 1 ≤ p ≤ 2, still regularizes the problem. Use of such ℓP 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 consideration. To compute the corresponding regularized solutions, we analyze an iterative algorithm that amounts to a Landweber iteration with thresholding (or nonlinear shrinkage) applied at each iteration step. We prove that this algorithm converges in norm. © 2004 Wiley Periodicals, Inc.


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