Audio Declipping with Unfolded Douglas-Rachford Algorithm

Abstract

This paper addresses the problem of audio declipping, which occurs when audio signals exceed a certain level, causing distortion and loss of information. To enhance existing methods, we propose a novel solution combining deep unfolding with the Douglas–Rachford algorithm (DRA) within an optimization framework, offering a blend of deep learning and optimization. The declipping problem is formulated as an optimization task that aims to recover the original signal by minimizing sparsity in the time-frequency domain. Our approach transforms each iteration of DRA into a layer of a neural network, optimizing parameters based on training data. Experimental results demonstrate that the unrolled DRA (uDRA) achieves short inference time compared to classical declipping methods, although it does not yet match them in terms of restoration quality. This work highlights the potential of deep unfolding for efficient audio declipping, with future improvements needed to capture the complexities of audio distortion more effectively.