replica method

Phase diagram and approximate message passing for blind calibration and dictionary learning

We consider dictionary learning and blind calibration for signals and matrices created from a random ensemble. We study the mean-squared error in the limit of large signal dimension using the replica method and unveil the appearance of phase …

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 …