A dereverberation formulation based on sparsity

The dereverberation problem can be cast as a sparsity-based minimization problem, by making use of the short-time Fourier transform (STFT), provided that the room impulse response is known. However, in such a formulation, especially if the room impulse response is longer than the window employed in the STFT, minimization of the resulting cost function requires the STFT operator at each iteration. This in turn increases the computation cost of the minimization task. In this paper, we propose a formulation which can be solved by a simple iterative algorithm that does not require the use of the STFT operator. We also investigate the performance of the formulation in a scenario where a real room impulse response is used.