Audio Soft Declipping Based on Constrained Weighted Least Squares

This letter presents a novel approach to blind recovery of audio signals that have been distorted by a memoryless, invertible, and smooth nonlinear function. We introduce a cost function consisting of a weighted sum of squared discrete cosine transform coefficients of the recovered signal, whose weights are obtained from the distorted signal itself and, thus, can adapt to different signal characteristics. In order to prevent undesired trivial solutions, we impose an either quadratic or linear equality constraint, the latter case with closed-form solution. Despite its simplicity, our method outperforms a recent sparsity-based solution for memoryless nonlinearity compensation, in audio and speech databases.