Consistent dictionary learning for signal declipping

Clipping, or saturation, is a common nonlinear distortion in signal processing. Recently, declipping techniques have been proposed based on sparse decomposition of the clipped signals on a fixed dictionary, with additional constraints on the amplitude of the clipped samples. Here we propose a dictionary learning approach, where the dictionary is directly learned from the clipped measurements. We propose a soft-consistency metric that minimizes the distance to a convex feasibility set, and takes into account our knowledge about the clipping process. We then propose a gradient descent-based dictionary learning algorithm that minimizes the proposed metric, and is thus consistent with the clipping measurement. Experiments show that the proposed algorithm outperforms other dictionary learning algorithms applied to clipped signals. We also show that learning the dictionary directly from the clipped signals outperforms consistent sparse coding with a fixed dictionary