A compression-based backward approach for the forward sparse modeling with application to speech coding

This paper concentrates on the development of an efficient and robust backward solution for the forward sparse greedy algorithms and applies this solution in the field of speech compression. All existing backward solutions are based on constraining more and more weights to zero while re-optimizing the remaining nonzero weights to compensate. Our approach is termed Backward Replacement (BRe) algorithm and its idea is to replace the k−sparse weights vector with a k−sparse symmetric matrix. The key result of this paper showed that, the replacement approach has demonstrated successfully the superiority over existing backward elimination algorithms in both enhancing the compression capabilities of the forward greedy algorithms, and reducing the time complexity.