Countering the false myth of democracy: Boosting compressed sensing performance with maximum-energy approach

Compressed Sensing (CS) is an effective way to sample a signal at a sub-Nyquist rate, i.e., by using a number of measurements smaller than the number of samples required when using the standard Nyquist approach. Measurements are obtained as linear projections of input signals along random sensing vectors. CS has been often regarded as a democratic method, in the sense that each measurement contributes to signal reconstruction with a similar amount of information. In this paper, by combining empirical observations with results from recent papers, we propose a different point of view, and show that CS is an oligarchic approach where performance is basically set by the measurements with the highest energy. This allows us to propose a new CS-based approach that bases the reconstruction on the maximum-energy measurements only and improves the compression performance with respect to classical approaches.