Single-channel blind dereverberation based on sparse matrix recovery with reweighting and accelerated alternating direction method of multipliers

Single-channel blind dereverberation aims to remove reverberation from a single-channel reverberant signal without using any prior knowledge. In acoustics, weighted prediction error (WPE), a method mainly used for a multi-channel signal, is often applied for this task. However, it is difficult to achieve well-performed dereverberation for a single-channel signal. In this paper, for better single-channel dereverberation, we propose to simultaneously estimate the source signal and the room impulse response (RIR) instead of only predicting reverberation. By modeling convolution using matrix lifting in the time-frequency domain, we formulate the dereverberation problem as a non-convex optimization problem of recovering a sparse rank-1 matrix. In sparse regularization, we introduce reweighting, enabling the improvement of sparse matrix recovery. The alternating direction method of multipliers (ADMM) with acceleration is applied to approximately solve the optimization problem, resulting in closed form updates. In our experiments, we confirmed that the proposed method outperforms existing methods in several reverberant conditions and is capable of removing both early reflection and late reverberation. MATLAB code of the proposed method is available online (https://doi.org/10.24433/CO.3541617.v1).