q-ary Compressive Sensing

摘要

We introduce q-ary compressive sensing, an extension of 1-bit compressive sensing. We propose a novel sensing mechanism and a corresponding recovery procedure. The recovery properties of the proposed approach are analyzed both theoretically and empirically. Results in 1-bit compressive sensing are recovered as a special case. Our theoretical results suggest a tradeoff between the quantization parameter q and the number of measurements m, in controlling the error and robustness to noise of the resulting recovery algorithm.