Harmonic/Percussive Source Separation Based on Anisotropic Smoothness of Magnitude Spectrograms via Convex Optimization

Harmonic/percussive source separation (HPSS) is an important tool for analyzing and processing audio signals. The standard approach to HPSS takes advantage of the structural difference of sinusoidal and percussive components, called
anisotropic smoothness
, in magnitude spectrograms. However, the existing methods disregard phase of the spectrograms and/or approximate the problem, which naturally limits the upper bound of the performance of HPSS. In this paper, we propose a novel approach to HPSS that regards phase without the approximation. The proposed method introduces an auxiliary variable that acts as an adaptive weight of a weighted energy minimization problem, which enables us to apply smoothing on magnitude of complex-valued spectrograms. Compared to the existing methods, the proposed method can obtain separated components having better magnitude and phase by simultaneously handling them.