A variational EM algorithm for the separation of moving sound sources

Abstract

This paper addresses the problem of separation of moving sound sources. We propose a probabilistic framework based on the complex Gaussian model combined with non-negative matrix factorization. The properties associated with moving sources are modeled using time-varying mixing filters described by a stochastic temporal process. We present a variational expectation-maximization (VEM) algorithm that employs a Kalman smoother to estimate the mixing filters. The sound sources are separated by means of Wiener filters, built from the estimators provided by the proposed VEM algorithm. Preliminary experiments with simulated data show that, while for static sources we obtain results comparable with the baseline method [1], in the case of moving source our method outperforms a piece-wise version of the baseline method.

Audio source separation into the wild

“…In [65,67], the transfer function of the mixing filters were considered as continuous latent variables ruled by a first-order linear dynamical system (LDS) with Gaussian noise [17], in the spirit of [47]. This model was used in combination with a source LGM-with-NMF model, still to process underdetermined time-varying convolutive mixtures.…”

Low Latency and High Quality Two-Stage Human-Voice-Enhancement System for a Hose-Shaped Rescue Robot

“…The conventional online BSS methods, which separate sound sources based on the phase differences among microphones, assume that the array layout is stable or known in advance [14,19,20]. Although there are several offline BSS methods that track the time-varying phase differences or array layout [21], it is difficult to conduct such tracking in real time and in an online manner.…”

Phase unmixing: Multichannel source separation with magnitude constraints

“…While (ΦLS) assumes that source magnitudes are known, MWF assumes that source variances are known, which is the same quantity of 1 Solving one instance of (ΦLS) using the Matlab version of BARON [23] on a regular laptop takes over a minute with M = 2, K = 3. 2 In the under-determined case, the expression (3) is equivalently replaced by Diag{b} 2 A H (ADiag{b} 2 A H + σ 2 n I M ) −1 y for numerical stability.…”

“…Due to these ambiguities, source separation under various prior knowledge on A, s 0 or n is a long-standing and still active research topic. Often, specific structures are imposed on A based on physical [1,2] or learned [3] models of signal propagation. It is also quite common to add statistical assumptions on source and noise signals.…”