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 majorization-equalization 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.
Highlights
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
As a state-of-the-art Independent component analysis (ICA)-based BSS method, Kitamura et al proposed independent low-rank matrix analysis (ILRMA) [10], [14], which is a unification of independent vector analysis (IVA) and nonnegative matrix factorization (NMF) [15]
T-ILRMA [11] and GGD-ILRMA [12], [13] have been proposed as generalizations of IS-ILRMA with a complex Student’s t distribution and a complex generalized Gaussian distribution (GGD) [19], respectively. Their update rules for the demixing matrix can be derived by a combined technique of the majorization-minimization (MM) algorithm [20] and iterative projection (IP), where IP is a fast and convergence-guaranteed algorithm introduced first for auxiliary-function-based ICA (AuxICA) [8] and auxiliary-function-based IVA (AuxIVA) [9]
Summary
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. T-ILRMA [11] and GGD-ILRMA [12], [13] have been proposed as generalizations of IS-ILRMA with a complex Student’s t distribution and a complex generalized Gaussian distribution (GGD) [19], respectively Their update rules for the demixing matrix can be derived by a combined technique of the majorization-minimization (MM) algorithm [20] and iterative projection (IP), where IP is a fast and convergence-guaranteed algorithm introduced first for auxiliary-function-based ICA (AuxICA) [8] and auxiliary-function-based IVA (AuxIVA) [9]. This is so in GGD-ILRMA because the estimation algorithm for the demixing matrix has not yet been derived for a sub-Gaussian case, the GGD itself can represent a subGaussian distribution depending on its shape parameter.
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