Non-uniform compressive sensing

In this paper, we introduce non-uniform compressive sensing (NCS), a novel compressive sensing (CS) technique that enables non-uniform recovery of sparse signals coefficients from their undersampled random projections. This is in contrast to the conventional CS techniques and is of great interest in many practical applications in which coefficients of a signal may have unequal importance levels. We design NCS by modifying the CS sampling phase and our simulation results indicate that by properly tuning the parameters of NCS, desired non-uniform recovery is attainable. The coefficients with more importance are recovered with a higher probability compared to uniform CS, in return for a slight performance loss in the recovery of less important coefficients. To make the theoretical analysis of NCS tractable, we further study NCS under a simple decoder and confirm that desired non-uniform recovery can be achieved by NCS. Moreover, we demonstrate that NCS can provide unequal recovery time. This means that different parts of signal x can reach a target reconstruction quality at different time spans from the beginning of the measurement stream. NCS is mainly inspired by a previous work by Rahnavard et al. on unequal-error- protection rateless codes.