Average recovery performances of non-perfectly informed compressed sensing: With applications to multiclass encryption

The sensitivity of recovery algorithms with respect to a perfect knowledge of the encoding matrix is a general issue in many application scenarios in which compressed sensing is an option to acquire or encode natural signals. Quantifying this sensitivity in order to predict the result of signal recovery is therefore valuable when no a priori information can be exploited, e.g., when the encoding matrix is randomly perturbed without any exploitable structure. We tackle this aspect by means of a simplified model for the signal recovery problem, which enables the derivation of an average performance estimate that depends only on the interaction between the sensing and perturbation matrices. The effectiveness of the resulting heuristic is demonstrated by numerical exploration of signal recovery under three simple perturbation matrix models. Finally, we show how this estimate matches very well the degradation experienced by non-perfectly informed decoders in applications of compressed sensing to protecting the acquired information content in ECG tracks and sensitive images.