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

Fast Iterative Shrinkage for Signal Declipping and Dequantization