Publications [#287169] of Ingrid Daubechies

Papers Published

1. 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. 1413-1457, WILEY [doi]
   (last updated on 2026/01/14)

   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 ℓ^P - penalties on the coefficients of such expansions, with 1 ≤ p ≤ 2, still regularizes the problem. Use of such ℓ^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 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.