Quantization of Sparse Representations
Boufounos, Petros T.
Baraniuk, Richard G.
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 effect of quanitization of CS measurements. A careful study of stictly sparse, power-limited signals concludes that CS with scalar quantization does not use its allocated rate efficiently. The inefficiency, which is quantified, can be interpreted as the price that must be paid for the universality of the encoding system. The results in this paper complement and extend recent results on the quantization of compressive sensing measurements of compressible signals.