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

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 L2(R) are also displayed for several test-cases. Finally, some algorithms are studied for the treatment of zero-angle problems.