Performance analysis of generalized block diagonal structured random matrices in compressive sensing

In compressive sensing practice, the choice of compression matrix reflects the important tradeoffs between the reconstruction performance and the implementation cost. Motivated by practical signal processing applications, this paper advocates a family of generalized block diagonal (GBD) structured random matrices for the implementation simplicity and reduced memory requirements. The restricted isometry property of such structured matrices is established to reveal the minimum number of measurements required for the perfect reconstruction of a sparse signal with high probability. The reconstruction performance of GBD random matrices is compared with that of conventional dense random matrices via both the theoretical derivation and the empirical simulations. For moderate-size sparse signals, the GBD random matrices are shown to enjoy several nice structural benefits in practical implementations, at minimal extra cost in terms of the number of required measurements.