ICA of Noisy Music Audio Mixtures Based on Iterative Shrinkage Denoising and FastICA Using Rational Nonlinearities

Blind source separation (BSS) has an extensive application prospect in many fields, and independent component analysis (ICA) is a very effective tool for solving the BSS problem. Noisy BSS/ICA, as it approaches the reality, is frequently considered in many practical applications. In this paper, we mainly discuss the "sensor" noise, adding Gaussian white noise to the music audio mixtures. To solve noisy BSS/ICA problem, we deploy denoising pre-processing before performing FastICA. Rather than traditional wavelet shrinkage, we employ a more advanced shrinkage denoising algorithm, parallel coordinate descent (PCD) iterative shrinkage based on redundant dictionary, to accomplish the denoising task. Since the classical nonlinearities (tanh and gauss) used in FastICA are not the optimal ones due to their slow computational speed, we propose two novel rational nonlinearities that have faster computational speed and almost the same or better separation performance comparing with the classical ones. As they originate from Pade approximant of tanh and gauss, but the coefficients are adjusted, we name them Variant Tanh Pade (VTP) and Variant Gauss Pade (VGP), respectively.