Performance bounds for sparsity pattern recovery with quantized noisy random projections

In this paper, we study the performance limits of recovering the support of a sparse signal based on quantized noisy random projections. Although the problem of support recovery of sparse signals with real valued noisy projections with different types of projection matrices has been addressed by several authors in the recent literature, very few attempts have been made for the same problem with quantized compressive measurements. In this paper, we derive performance limits of support recovery of sparse signals when the quantized noisy corrupted compressive measurements are sent to the decoder over additive white Gaussian noise channels. The sufficient conditions which ensure the perfect recovery of sparsity pattern of a sparse signal from coarsely quantized noisy random projections are derived when the maximum-likelihood decoder is used. More specifically, we find the relationships among the parameters, namely the signal dimension $N$ , the sparsity index $K$ , the number of noisy projections $M$, the number of quantization levels $L$, and measurement signal-to-noise ratio which ensure the asymptotic reliable recovery of the support of sparse signals when the entries of the measurement matrix are drawn from a Gaussian ensemble.