Recovering Compressively Sampled Signals Using Partial Support Information

TL;DR

This paper demonstrates that weighted  minimization leveraging partial support information improves signal recovery in compressed sensing, especially when the support info is at least 50% accurate, leading to better stability and error bounds.

Contribution

It establishes weaker recovery conditions and enhanced error bounds for weighted  minimization with partial support info, supported by extensive numerical experiments.

Findings

Weighted  minimization is stable with at least 50% accurate support info.

Improved bounds on reconstruction error over standard  minimization.

Validates theoretical results with experiments on synthetic and real data.

Abstract

In this paper we study recovery conditions of weighted $\ell_1$ minimization for signal reconstruction from compressed sensing measurements when partial support information is available. We show that if at least 50% of the (partial) support information is accurate, then weighted $\ell_1$ minimization is stable and robust under weaker conditions than the analogous conditions for standard $\ell_1$ minimization. Moreover, weighted $\ell_1$ minimization provides better bounds on the reconstruction error in terms of the measurement noise and the compressibility of the signal to be recovered. We illustrate our results with extensive numerical experiments on synthetic data and real audio and video signals.