Fast Iterative Shrinkage for Signal Declipping and Dequantization

We address the problem of recovering a sparse signal from clipped or quantized measurements. We show how these two problems can be formulated as minimizing the distance to a convex feasibility set, which provides a convex and differentiable cost function. We then propose a fast iterative shrinkage/thresholding algorithm that minimizes the proposed cost, which provides a fast and efficient algorithm to recover sparse signals from clipped and quantized measurements.