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Corrupted sensing concerns the problem of recovering a high-dimensional structured signal from a collection of measurements that are contaminated by unknown structured corruption and unstructured noise. In the case of linear measurements, the recovery performance of different convex programming procedures (e.g., generalized Lasso and its variants) is well established in the literature. However, in practical applications of digital signal processing, the quantization process is inevitable, which often leads to non-linear measurements. This paper is devoted to studying corrupted sensing under quantized measurements. Specifically, we demonstrate that, with the aid of uniform dithering, both constrained and unconstrained Lassos are able to recover signal and corruption from the quantized samples when the measurement matrix is sub-Gaussian. Our theoretical results reveal the role of quantization resolution in the recovery performance of Lassos. Numerical experiments are provided to confirm our theoretical results.
Quantized compressive sensing (QCS) deals with the problem of coding compressive measurements of low-complexity signals with quantized, finite precision representations, i.e., a mandatory process involved in any practical sensing model. While the res
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This paper studies the problem of accurately recovering a structured signal from a small number of corrupted sub-Gaussian measurements. We consider three different procedures to reconstruct signal and corruption when different kinds of prior knowledg