Blind separation of underdetermined mixtures with additive white and pink noises

This paper presents an approach for underdetermined blind source separation in the case of additive Gaussian white noise and pink noise. Likewise, the proposed approach is applicable in the case of separating I + 3 sources from I mixtures with additive two kinds of noises. This situation is more challenging and suitable to practical real world problems. Moreover, unlike to some conventional approaches, the sparsity conditions are not imposed. Firstly, the mixing matrix is estimated based on an algorithm that combines short time Fourier transform and rough-fuzzy clustering. Then, the mixed signals are normalized and the source signals are recovered using modified Gradient descent Local Hierarchical Alternating Least Squares Algorithm exploiting the mixing matrix obtained from the previous step as an input and initialized by multiplicative algorithm for matrix factorization based on alpha divergence. The experiments and simulation results show that the proposed approach can separate I + 3 source signals from I mixed signals, and it has superior evaluation performance compared to some conventional approaches

Differential fast fixed-point algorithms for underdetermined instantaneous and convolutive partial blind source separation

This paper concerns underdetermined linear instantaneous and convolutive blind source separation (BSS), i.e., the case when the number of observed mixed signals is lower than the number of sources.We propose partial BSS methods, which separate supposedly nonstationary sources of interest (while keeping residual components for the other, supposedly stationary, "noise" sources). These methods are based on the general differential BSS concept that we introduced before. In the instantaneous case, the approach proposed in this paper consists of a differential extension of the FastICA method (which does not apply to underdetermined mixtures). In the convolutive case, we extend our recent time-domain fast fixed-point C-FICA algorithm to underdetermined mixtures. Both proposed approaches thus keep the attractive features of the FastICA and C-FICA methods. Our approaches are based on differential sphering processes, followed by the optimization of the differential nonnormalized kurtosis that we introduce in this paper. Experimental tests show that these differential algorithms are much more robust to noise sources than the standard FastICA and C-FICA algorithms.Comment: this paper describes our differential FastICA-like algorithms for linear instantaneous and convolutive underdetermined mixture

Scalable transformed additive signal decomposition by non-conjugate Gaussian process inference

Many functions and signals of interest are formed by the addition of multiple underlying components, often nonlinearly transformed and modified by noise. Examples may be found in the literature on Generalized Additive Models [1] and Underdetermined Source Separation [2] or other mode decomposition techniques. Recovery of the underlying component processes often depends on finding and exploiting statistical regularities within them. Gaussian Processes (GPs) [3] have become the dominant way to model statistical expectations over functions. Recent advances make inference of the GP posterior efficient for large scale datasets and arbitrary likelihoods [4,5]. Here we extend these methods to the additive GP case [6, 7], thus achieving scalable marginal posterior inference over each latent function in settings such as those above

Extracting individual contributions from their mixture: a blind source separation approach, with examples from space and laboratory plasmas

Multipoint or multichannel observations in plasmas can frequently be modelled as an instantaneous mixture of contributions (waves, emissions, ...) of different origins. Recovering the individual sources from their mixture then becomes one of the key objectives. However, unless the underlying mixing processes are well known, these situations lead to heavily underdetermined problems. Blind source separation aims at disentangling such mixtures with the least possible prior information on the sources and their mixing processes. Several powerful approaches have recently been developed, which can often provide new or deeper insight into the underlying physics. This tutorial paper briefly discusses some possible applications of blind source separation to the field of plasma physics, in which this concept is still barely known. Two examples are given. The first one shows how concurrent processes in the dynamical response of the electron temperature in a tokamak can be separated. The second example deals with solar spectral imaging in the Extreme UV and shows how empirical temperature maps can be built.Comment: expanded version of an article to appear in Contributions to Plasma Physics (2010

Speech Separation Using Partially Asynchronous Microphone Arrays Without Resampling

We consider the problem of separating speech sources captured by multiple spatially separated devices, each of which has multiple microphones and samples its signals at a slightly different rate. Most asynchronous array processing methods rely on sample rate offset estimation and resampling, but these offsets can be difficult to estimate if the sources or microphones are moving. We propose a source separation method that does not require offset estimation or signal resampling. Instead, we divide the distributed array into several synchronous subarrays. All arrays are used jointly to estimate the time-varying signal statistics, and those statistics are used to design separate time-varying spatial filters in each array. We demonstrate the method for speech mixtures recorded on both stationary and moving microphone arrays.Comment: To appear at the International Workshop on Acoustic Signal Enhancement (IWAENC 2018

Weakly Supervised Audio Source Separation via Spectrum Energy Preserved Wasserstein Learning

Separating audio mixtures into individual instrument tracks has been a long standing challenging task. We introduce a novel weakly supervised audio source separation approach based on deep adversarial learning. Specifically, our loss function adopts the Wasserstein distance which directly measures the distribution distance between the separated sources and the real sources for each individual source. Moreover, a global regularization term is added to fulfill the spectrum energy preservation property regardless separation. Unlike state-of-the-art weakly supervised models which often involve deliberately devised constraints or careful model selection, our approach need little prior model specification on the data, and can be straightforwardly learned in an end-to-end fashion. We show that the proposed method performs competitively on public benchmark against state-of-the-art weakly supervised methods

Sparse Gaussian Process Audio Source Separation Using Spectrum Priors in the Time-Domain

Gaussian process (GP) audio source separation is a time-domain approach that circumvents the inherent phase approximation issue of spectrogram based methods. Furthermore, through its kernel, GPs elegantly incorporate prior knowledge about the sources into the separation model. Despite these compelling advantages, the computational complexity of GP inference scales cubically with the number of audio samples. As a result, source separation GP models have been restricted to the analysis of short audio frames. We introduce an efficient application of GPs to time-domain audio source separation, without compromising performance. For this purpose, we used GP regression, together with spectral mixture kernels, and variational sparse GPs. We compared our method with LD-PSDTF (positive semi-definite tensor factorization), KL-NMF (Kullback-Leibler non-negative matrix factorization), and IS-NMF (Itakura-Saito NMF). Results show that the proposed method outperforms these techniques.Comment: Paper submitted to the 44th International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019. To be held in Brighton, United Kingdom, between May 12 and May 17, 201