Semantic Scholar Open Access 2003 5312 sitasi

An iterative thresholding algorithm for linear inverse problems with a sparsity constraint

I. Daubechies M. Defrise C. D. Mol

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Abstrak

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 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.

Topik & Kata Kunci

Mathematics Computer Science

Penulis (3)

I. Daubechies

M. Defrise

C. D. Mol

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Daubechies, I., Defrise, M., Mol, C.D. (2003). An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. https://doi.org/10.1002/CPA.20042

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Informasi Jurnal

Tahun Terbit: 2003
Bahasa: en
Total Sitasi: 5312×
Sumber Database: Semantic Scholar
DOI: 10.1002/CPA.20042
Akses: Open Access ✓