Quantization of Sparse Representations

Petros Boufounos, Richard G. Baraniuk

Abstract: Compressive sensing (CS) is a new signal acquisition technique for sparse and compressible signals. Rather than uniformly sampling the signal, CS computes inner products with randomized basis functions; the signal is then recovered by a convex optimization. Random CS measurements are universal in the sense that the same acquisition system is sufficient for signals sparse in any representation. This paper examines the quantization of strictly sparse, power-limited signals and concludes that CS with scalar quantization uses its allocated rate inefficiently. The results complement related work on the quantization of CS measurements of compressible signals.