Room Impulse Response Reshaping and Crosstalk Cancellation Using Convex Optimization

In this article, a new convex formulation for the acoustic channel-equalization problem is proposed and efficient ways for solving it are presented. Both the alternating direction method of multipliers and a proximal algorithm are studied for optimization. Time-domain and frequency-domain constraints are included in an equal way, allowing for simultaneous reverberation reduction and frequency-response equalization. Rather than aiming at full channel equalization, we follow the channel-reshaping paradigm proposed in earlier works and try to push the reverberation tail under the temporal masking limit of the human auditory system, thus making reverberation inaudible for human listeners. While the algorithm is presented for the multiple-input-multiple-output (MIMO) scenario, the single-channel case is included as a special case. Comparisons with methods from the literature for the single- and multi-channel cases show that the new algorithm has faster convergence than the known ones. The proximal algorithm even allows for solving extremely large problems with very low memory demand.