A Donoho-Stark criterion for stable signal recovery in discrete wavelet subspaces

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:235

Article

Gosse, Laurent

关键词: Product of orthogonal projections;    Hilbert-Schmidt operator;    Geometric harmonics;    Singular operator with closed range;    Gradient algorithms;   

DOI  :  10.1016/j.cam.2011.04.034

来源: Elsevier

【 摘 要 】

We derive a sufficient condition by means of which one can recover a scale-limited signal from the knowledge of a truncated version of it in a stable manner following the canvas introduced by Donoho and Stark (1989) [4]. The proof follows from simple computations involving the Zak transform, well-known in solid-state physics. Geometric harmonics (in the terminology of Coifman and Lafon (2006) [22]) for scale-limited subspaces of L-2(R) are also displayed for several test-cases. Finally, some algorithms are studied for the treatment of zero-angle problems. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free