Fast reverberation-reduction algorithm based on inexact matrix decomposition

Traditionally, matrix-based methods for reverberation reduction have prioritized a high signal-to-reverberation ratio over low time consumption. This letter describes a fast reverberation-reduction algorithm. The reverberation-reduction problem is formulated as an inexact matrix decomposition. A low-rank matrix is obtained through the reverberation extraction in a low-dimensional matrix, and a two-stage structure optimizes the computation iterative frame. The proposed algorithm's convergence, time consumption, and error are numerically simulated. Field data processing results demonstrate that the algorithm achieves a similar receiver operating characteristic (ROC) curve as with the alternating direction multiplier method (ADMM) but reduces the time consumption by 33%.