Bayes-optimal reconstruction

Compressed sensing under matrix uncertainty: Optimum thresholds and robust approximate message passing

In compressed sensing one measures sparse signals directly in a compressed form via a linear transform and then reconstructs the original signal. However, it is often the case that the linear transform itself is known only approximately, a situation …

Compressed sensing of approximately-sparse signals: Phase transitions and optimal reconstruction

Compressed sensing is designed to measure sparse signals directly in a compressed form. However, most signals of interest are only “approximately sparse”, i.e. even though the signal contains only a small fraction of relevant (large) components the …