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Split Bregman Approach to Linear Prediction Based Dereverberation With Enforced Speech Sparsity

The recordings of speech in enclosures are corrupted by reverberation caused by multipath wave propagation from the speaker to the distant microphones. In this letter, we address the problem of reducing the late part of room reverberation. The presented blind dereverberation method consists in multichannel linear prediction (MCLP) and enforces sparsity of the dereverberated speech by adopting the split Bregman approach. The proposed algorithm alternately solves two optimization problems, where the former cost function is derived by assuming that speech is modelled using a sparse prior distribution, while the latter optimization emphasizes speech sparsity by an additional incorporation of a weighted $\ell _1$-norm of the output signal to the standard linear prediction based cost function. The results of experiments performed using simulated and measured room impulse responses for various reverberation time values indicate superior performance of the proposed sparse split Bregman (SSB) method over state-of-the-art non-sparse and sparse MCLP-based dereverberation methods in terms of standard evaluation measures and as pre-processsing to the automatic speech recognition.