Efficient parallel kernel based on Cholesky decomposition to accelerate multichannel nonnegative matrix factorization

Multichannel source separation has been a popular topic, and recently proposed methods based on the local Gaussian model have provided promising results despite its high computational cost when several sensors are used. This drawback limits the practical application of this approach to tasks such as sound field reconstruction or virtual reality. In this study, we presented a numerical approach to reduce the complexity of multichannel nonnegative matrix factorization to address the task of audio source separation for scenarios with a large number of sensors, such as high-order ambisonics encoding. In particular, we proposed a parallel driver to compute the multiplicative update rules in MNMF approaches. It is designed to function on both sequential and multicore computers, as well as graphics processing units (GPUs). The solution attempts to reduce the computational cost of multiplicative update rules by using Cholesky decomposition and solving several triangular equation systems. The driver was evaluated for different scenarios, with promising results in terms of execution times for both the CPU and GPU. To the best of our knowledge, this proposal is the first to address the problem of reducing the computational cost of full-rank MNMF-based systems using parallel and high-performance techniques.