Sparse coding and dictionary learning are popular techniques for linear inverse problems such as denoising or inpainting. However in many cases, the measurement process is nonlinear, for example for clipped, quantized or 1-bit measurements. These problems have often been addressed by solving constrained sparse coding problems, which can be difficult to solve, and assuming that the sparsifying dictionary is known and fixed. Here we propose a simple and unified framework to deal with nonlinear measurements. We propose a cost function that minimizes the distance to a convex feasibility set, which models our knowledge about the nonlinear measurement. This provides an unconstrained, convex, and differentiable cost function that is simple to optimize, and generalizes the linear least squares cost commonly used in sparse coding. We then propose proximal based sparse coding and dictionary learning algorithms, that are able to learn directly from nonlinearly corrupted signals. We show how the proposed framework and algorithms can be applied to clipped, quantized and 1-bit data.

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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 softconsistency 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.

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Text-based speech editors expedite the process of editing speech recordings by permitting editing via intuitive cut, copy, and paste operations on a speech transcript. A major drawback of current systems, however, is that edited recordings often sound unnatural because of prosody mismatches around edited regions. In our work, we propose a new context-aware method for more natural sounding textbased editing of speech. To do so, we 1) use a series of neural networks to generate salient prosody features that are dependent on the prosody of speech surrounding the edit and amenable to fine-grained user control 2) use the generated features to control a standard pitch-shift and time-stretch method and 3) apply a denoising neural network to remove artifacts induced by the signal manipulation to yield a highfidelity result. We evaluate our approach using a subjective listening test, provide a detailed comparative analysis, and conclude several interesting insights.