Entropy‐based learning of sensing matrices

Compressive sensing deals with non‐uniform sampling of a signal, at an average rate much less than the Nyquist rate, and recovery of the signal uniquely from these reduced set of measurements. Construction of an efficient measurement (sensing) matrix to enable unique recovery is a topic of interest since compressive sensing came to existence. The sensing operator should be efficient to capture the vital information content of the signal into a reduced set of discrete measurements. This study proposes a learning method to construct an efficient sensing matrix, having orthogonal rows, for compressed sensing of a class of signals. The learning scheme identifies the sensing matrix by maximising the entropy of measurement vectors. The bounds on the entropy of the measurement vector necessary for the unique recovery of a signal are proposed. A comparison of the performance of the designed sensing matrix and the sensing matrices constructed using other existing methods is also presented. The simulation results on the recovery of synthetic, speech, and image signals, compressively sensed using the sensing matrix identified, show an improvement in the accuracy of recovery. The reconstruction quality is better, using less number of measurements than those measured using sensing matrices identified by other methods.