Quantized Corrupted Sensing with Random Dithering

Quantized corrupted sensing concerns the problem of estimating structured signals from their quantized corrupted samples. A typical case is that when the measurements y = Φx^∗ + v^∗ + n are corrupted with both structured corruption v^∗ and unstructured noise n, we wish to reconstruct x^∗ and v^∗ from the quantized samples of y. Our work shows that the Generalized Lasso can be applied for the recovery of signal provided that a uniform random dithering is added to the measurements before quantization. The theoretical results illustrate that the influence of quantization behaves as independent unstructured noise. We also confirm our results numerically in several scenarios such as sparse vectors and low-rank matrices.