Abstract-In this paper, we propose a generalized scale mixture family of distributions, namely the Power Exponential Scale Mixture (PESM) family, to model the sparsity inducing priors currently in use for sparse signal recovery (SSR). We show that the successful and popular methods such as LASSO, Reweighted 1 and Reweighted 2 methods can be formulated in an unified manner in a maximum a posteriori (MAP) or Type I Bayesian framework using an appropriate member of the PESM family as the sparsity inducing prior. In addition, exploiting the natural hierarchical framework induced by the PESM family, we utilize these priors in a Type II framework and develop the corresponding EM based estimation algorithms. Some insight into the differences between Type I and Type II methods is provided and of particular interest in the algorithmic development is the Type II variant of the popular and successful reweighted 1 method. Extensive empirical results are provided and they show that the Type II methods exhibit better support recovery than the corresponding Type I methods.

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Neural network applications generally benefit from larger-sized models, but for current speech enhancement models, larger scale networks often suffer from decreased robustness to the variety of real-world use cases beyond what is encountered in training data. We introduce several innovations that lead to better large neural networks for speech enhancement. The novel PoCoNet architecture is a convolutional neural network that, with the use of frequency-positional embeddings, is able to more efficiently build frequency-dependent features in the early layers. A semi-supervised method helps increase the amount of conversational training data by pre-enhancing noisy datasets, improving performance on real recordings. A new loss function biased towards preserving speech quality helps the optimization better match human perceptual opinions on speech quality. Ablation experiments and objective and human opinion metrics show the benefits of the proposed improvements.

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