On quantized compressed sensing with saturated measurements via greedy pursuit

We consider the problem of signal recovery under a sparsity prior, from multi-bit quantized compressed measurements. Recently, it has been shown that allowing a small fraction of the quantized measurements to saturate, combined with a saturation consistency recovery approach, would enhance reconstruction performance. In this paper, by leveraging the potential sparsity of the corrupting saturation noise, we propose a model-based greedy pursuit approach, where a cancel-then-recover procedure is applied in each iteration to estimate the unbounded sign-constrained saturation noise and remove it from the measurements to enable a clean signal estimate. Simulation results show the performance improvements of our proposed method compared with state-of-the-art recovery approaches, in the noiseless and noisy settings.