The Restricted Isometry Property of the Radon-like CS matrix

In compressive sensing, the Restricted Isometry Property is an analytical condition on the measurement matrix that assures reconstruction of a signal which is sparse either in the spatial or in a transformed domain given an undersampled measurements´ set. In this paper, we demonstrate the RIP for a sparse, structured measurements matrix, referred to as Radon-like CS matrix. The sparse Radon-Like CS matrix favorably applies to real sensing problems, since it significantly reduces the energy/bandwidth cost of actually collecting each and every sensed values contributing to the CS measurements. Simulation results confirm the feasibility of field reconstruction from undersampled CS measurements set obtained using the Radon-Like CS matrix.