An efficient parallel kernel based on Cholesky decomposition to accelerate Multichannel Non-Negative Matrix Factorization

Abstract

Multichannel Source Separation has been a popular topic, and recently proposed methods based on the local Gaussian model (LGM) have provided promising result despite its high computational cost when several sensors are used. The main reason being due to inversion of a spatial covariance matrix, with a complexity of \(O(I^3)\), being \(I\) the number of sensors. This drawback limits the practical application of this approach for tasks such as sound field reconstruction or virtual reality, among others. In this paper, we present a numerical approach to reduce the complexity of the Multichannel NMF to address the task of audio source separation for scenarios with a high number of sensors such as High Order Ambisonics (HOA) encoding. In particular, we propose a parallel multi-architecture driver to compute the multiplicative update rules in MNMF approaches. The proposed driver has been designed to work on both sequential and multi-core computers, as well as Graphics Processing Units (GPUs) and Intel Xeon coprocessors. The proposed software was written in C language and can be called from numerical computing environments. The proposed solution tries to reduce the computational cost of the multiplicative update rules by using the Cholesky decomposition and by solving several triangular equation systems.The proposal has been evaluated for different scenarios with promising results in terms of execution times for both CPU and GPU. To the best of our knowledge, our proposal is the first system that addresses the problem of reducing the computational cost of full-rank MNMF-based systems using parallel and high performance techniques.