Abstract
Blind deconvolution is an ill-posed problem. To solve such a prob- lem, prior information, such as, the sparseness of the source (i.e. input) signal or channel impulse responses, is usually adopted. In speech deconvolution, the source signal is not naturally sparse. However, the direct impulse and early reflections of the impulse responses of an acoustic system can be considered as sparse. In this paper, we exploit the channel sparsity and present an algorithm for speech deconvolution, where the dynamic range of the convolutive speech is also used as the prior information. In this algorithm, the estimation of the impulse response and the source signal is achieved by alternating between two steps, namely, the ℓ1 regularized least squares optimization and a proximal operation. As demonstrated in our experiments, the proposed method pro- vides superior performance for deconvolution of a sparse acoustic system, as compared with two state-of-the-art methods.