“Applied Mathematics”

$(\ell_{1},\ell_{2})$-RIP and Projected Back-Projection Reconstruction for Phase-Only Measurements

Abstract: This letter analyzes the performances of a simple reconstruction method, namely the Projected Back-Projection (PBP), for estimating the direction of a sparse signal from its phase-only (or amplitude-less) complex Gaussian random measurements, i.

Jointly low-rank and bisparse recovery: Questions and partial answers

Abstract: We investigate the problem of recovering jointly \(r\)-rank and \(s\)-bisparse matrices from as few linear measurements as possible, considering arbitrary measurements as well as rank-one measurements. In both cases, we show that \(m \asymp r s \ln(en/s)\) measurements make the recovery possible in theory, meaning via a nonpractical algorithm.