Rate-Distortion Theory of Distributed Compressed Sensing

In this chapter, correlated and distributed sources without cooperation at the encoder are considered. For these sources, the best achievable performance in the rate-distortion sense of any distributed compressed sensing scheme is derived, under the constraint of high-rate quantization. Moreover, under this model we derive a closed-form expression of the rate gain achieved by taking into account the correlation of the sources at the receiver and a closed-form expression of the average performance of the oracle receiver for independent and joint reconstruction. Finally, we show experimentally that the exploitation of the correlation between the sources performs close to optimal and that the only penalty is due to the missing knowledge of the sparsity support as in (non-distributed) compressed sensing. Even if the derivation is performed in the large system regime, where signal and system parameters tend to infinity, numerical results show that the equations match simulations for parameter values of practical interest.