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

Laurent Gosse (1)

1 IAC - Istituto per le Applicazioni del Calcolo "Mauro Picone"

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 \cite{DS}. The proof follows from simple computations involving the Zak transform, well-known in solid-state physics. Geometric harmonics (in the terminology of \cite{CL}) for scale-limited subspaces of $L^2(\Re)$ are also displayed for several test-cases. Finally, some algorithms are studied for the treatment of zero-angle problems.

Mots clés: Product of orthogonal projections; Hilbert-Schmidt operator; Geometric harmonics; Singular operator with closed range; Gradient algorithms.; Gradient algorithms

Domaines: Analyse numérique [math.NA]; Applications [stat.AP]; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Laurent Gosse. A Donoho-Stark criterion for stable signal recovery in discrete wavelet subspaces. Journal of Computational and Applied Mathematics, 2011, 235, pp.5024-5039. ⟨10.1016/j.cam.2011.04.034⟩. ⟨hal-00508932⟩