Independent Low-Rank Matrix Analysis Based on Time-Variant Sub-Gaussian Source Model for Determined Blind Source Separation

Abstract

Independent low-rank matrix analysis (ILRMA) is a fast and stable method of blind audio source separation. Conventional ILRMAs assume time-variant (super-)Gaussian source models, which can only represent signals that follow a super-Gaussian distribution. In this article, we focus on ILRMA based on a generalized Gaussian distribution (GGD-ILRMA) and propose a new type of GGD-ILRMA that adopts a time-variant sub-Gaussian distribution for the source model. We propose a new update scheme called generalized iterative projection for homogeneous source models (GIP-HSM) and obtain a convergence-guaranteed update rule for demixing spatial parameters by combining the GIP-HSM scheme and the majorization-minimization (MM) algorithm. Furthermore, a new extension of the MM algorithm is proposed for the convergence acceleration by applying the majorizationequalization algorithm to a multivariate case. In the experimental evaluation, we show the versatility of the proposed method, i.e., the proposed time-variant sub-Gaussian source model can be applied to various types of source signal. Index Terms-Blind source separation, independent low-rank matrix analysis (ILRMA), generalized Gaussian distribution. I. INTRODUCTION B LIND source separation (BSS) [1]-[14] is a technique of extracting specific sources from an observed multichannel mixture signal without knowing a priori information about the mixing system. Independent component analysis (ICA) and its extensions, such as independent vector analysis (IVA) [5], [6], are the most commonly used approaches for BSS in an

Noise Robust Acoustic Anomaly Detection System with Nonnegative Matrix Factorization Based on Generalized Gaussian Distribution

“…In the generative model (8), the complex GGD is independently defined in each time-frequency slot, and its scale parameter σ i j can fluctuate along time and frequency axes. In this case, the macro model that includes all the timefrequency slots, i.e., the generative model of the spectrogram C, always approaches to a super-Gaussian distribution when σ i j dynamically varies along i and j [16]. For this reason, the generative model (8) with sub-Gaussian GGD (ρ > 2) has a versatility as depicted in Fig.…”

Consistent Independent Low-Rank Matrix Analysis for Determined Blind Source Separation

“…where e n ∈ {0, 1} N is the unit vector with the nth element equal to unity. The update rules (19)-(24) ensure the monotonic non-increase of the negative log-likelihood function L. After iterative calculations of these updates (19)- (24), the separated signal can be obtained by (12).…”

Consistent independent low-rank matrix analysis for determined blind source separation

“…Its combination with stateof-the-art models, including ILRMA, is of great interest because the current mainstream algorithm for determined audio source separation is centered on ILRMA, which is based on an NMF-based richer time-frequency source model. Indeed, many recent papers are based on the framework of ILRMA [17][18][19][20][21][22][23][24][25][26][27][28][29]. Even though combining ILRMA with the spectrogram consistency should be able to exceed the limit of existing BSS algorithms, no such method has been investigated in the literature.…”

“…However, in ILRMA, since both the demixing matrix W i and the source model parameter T n V n can determine the scale of estimated signal Y n , the likelihood variation can be avoided by appropriately adjusting w in and T n after the back projection. To prevent the likelihood variation, the following updates are required after performing (26):…”

“…This extension has greatly improved the performance of separation by taking the low-rank time-frequency structure (co-occurrence among the time-frequency bins) of the source signals into account. ILRMA has achieved the state-of-the-art performance and been further developed by several researchers [17][18][19][20][21][22][23][24][25][26][27][28][29]. In this respect, ILRMA can be considered the new standard of the determined BSS algorithms.…”