Clipping or saturation in audio signals is a very common problem in signal processing, for which, in the severe case, there is still no satisfactory solution. In such case, there is a tremendous loss of information, and traditional methods fail to appropriately recover the signal. We propose a novel approach for this signal restoration problem based on the framework of Iterative Hard Thresholding. This approach, which enforces the consistency of the reconstructed signal with the clipped observations, shows superior performance in comparison to the state-of-the-art declipping algorithms. This is confirmed on synthetic and on actual high-dimensional audio data processing, both on SNR and on subjective user listening evaluations.

This article is a survey of deep learning methods for single and multiple sound source localization, with a focus on sound source localization in indoor environments, where reverberation and diffuse noise are present. We provide an extensive topography of the neural network-based sound source localization literature in this context, organized according to the neural network architecture, the type of input features, the output strategy (classification or regression), the types of data used for model training and evaluation, and the model training strategy. Tables summarizing the literature survey are provided at the end of the paper, allowing a quick search of methods with a given set of target characteristics.

Sparse data models are powerful tools for solving illposed inverse problems. We present a regularization framework based on the sparse synthesis and sparse analysis models for problems governed by linear partial differential equations. Although nominally equivalent, we show that the two models differ substantially from a computational perspective: unlike the sparse synthesis model, its analysis counterpart has much better scaling capabilities and can indeed be faster when more measurement data is available. Our findings are illustrated on two examples, sound source localization and brain source localization, which also serve as showcases for the regularization framework. To address this type of inverse problems, we develop a specially tailored convex optimization algorithm based on the Alternating Direction Method of Multipliers.

Indoor acoustic source localization can be efficiently performed by modeling the sound propagation in the room, and by solving the arising inverse problem by means of cosparse regularization and convex optimization techniques. However, previous methods relying on this approach used to assume the knowledge of a number of room characteristics: its geometry, the walls' absorption or reflexion properties, as well as the speed of sound. In this paper, we show that this model, and the corresponding algorithms, can be extended to the case where the specific acoustic impedance of the boundary is unknown. The proposed method allows to jointly estimate the boundary impedances and the sound pressure in the room, without any preliminary calibration phase, from the only knowledge of the room geometry. Validated on simulation, this new algorithm constitutes a important step towards practical applicability of sound field cosparse modeling.