1-bit Hamming compressed sensing

Compressed sensing (CS) and 1-bit CS cannot directly recover quantized signals preferred in digital systems and require time consuming recovery. In this paper, we introduce 1-bit Hamming compressed sensing (HCS) that directly recovers a k-bit quantized signal of dimension n from its 1-bit measurements via invoking n times of Kullback-Leibler divergence based nearest neighbor search. Compared to CS and 1-bit CS, 1-bit HCS allows the signal to be dense, takes considerably less (linear and non-iterative) recovery time and requires substantially less measurements. Moreover, 1-bit HCS can accelerate 1bit CS recover. We study a quantized recovery error bound of 1-bit HCS for general signals. Extensive numerical simulations verify the appealing accuracy, robustness, efficiency and consistency of 1-bit HCS.