Improving sign-algorithm convergence rate using natural gradient for lossless audio compression

Abstract

In lossless audio compression, the predictive residuals must remain sparse when entropy coding is applied. The sign algorithm (SA) is a conventional method for minimizing the magnitudes of residuals; however, this approach yields poor convergence performance compared with the least mean square algorithm. To overcome this convergence performance degradation, we propose novel adaptive algorithms based on a natural gradient: the natural-gradient sign algorithm (NGSA) and normalized NGSA. We also propose an efficient natural-gradient update method based on the AR(p) model, which requires mathcal {O}(p) multiply–add operations at every adaptation step. In experiments conducted using toy and real music data, the proposed algorithms achieve superior convergence performance to the SA. Furthermore, we propose a novel lossless audio codec based on the NGSA, called the natural-gradient autoregressive unlossy audio compressor (NARU), which is open-source and implemented in C. In a comparative experiment with existing, well-known codecs, NARU exhibits superior compression performance. These results suggest that the proposed methods are appropriate for practical applications.