Conventional algorithms for blind source separation do not necessarily work well for real-world data. One of the reasons is that, in actual applications, the mixing matrix is often almost singular at some part of frequency range and it can cause a certain computational instability. This paper proposes a new algorithm to overcome this singularity problem. The algorithm is based on the minimal di...

Existing methods for frequency-domain estimation of mixing filters in convolutive blind source separation (BSS) suffer from permutation and scaling indeterminacies in sub-bands. However, if the filters are assumed to be sparse in the time domain, it is shown in this paper that the !1-norm of the filter matrix increases as the sub-band coefficients are permuted. With this motivation, an algorith...

Blind Source Separation (BSS) is a challenging matrix factorization problem that plays a central role in multichannel imaging science. In a large number of applications, such as astrophysics, current unmixing methods are limited since real-world mixtures are generally affected by extra instrumental effects like blurring. Therefore, BSS has to be solved jointly with a deconvolution problem, whic...

Using the sparsity property in the frequency domain of harmonic signals, this paper gives a harmonic extraction algorithm based on multi-resolution blind source separation (BSS) method. After the general and detailed definition of the multi-resolution BSS model is given, the wavelet packet decomposition based multiresolution BSS algorithm for harmonic signal extraction is constructed in detail....

We consider a problem of blind source separation from a set of instantaneous linear mixtures, where the mixing matrix is unknown. It was discovered recently, that exploiting the sparsity of sources in an appropriate representation according to some signal dictionary, dramatically improves the quality of separation. In this work we use the property of multi scale transforms, such as wavelet or w...

In this paper, we consider the nonlinear Blind Source Separation BSS and independent component analysis (ICA) problems, and especially uniqueness issues, presenting some new results. A fundamental di6culty in the nonlinear BSS problem and even more so in the nonlinear ICA problem is that they are nonunique without a suitable regularization. In this paper, we mainly discuss three di8erent ways f...

Robust clustering of data into overlapping linear subspaces is a common problem. Here we consider one-dimensional subspaces that cross the origin. This problem arises in blind source separation, where the subspaces correspond directly to columns of a mixing matrix. We present an algorithm that identifies these subspaces using an EM procedure, where the E-step calculates posterior probabilities ...

This paper is a survey of semi-blind source separation approaches. Since Gaussian iid signals are not separable, simplest priors suggest to assume non Gaussian iid signals, or Gaussian non iid signals. Other priors can also been used, for instance discrete or bounded sources, positivity, etc. Although providing a generic framework for semi-blind source separation, Sparse Component Analysis and ...

SUMMARY This paper deals with the problem of underdetermined blind source separation (BSS) where the number of sources is unknown. We propose a BSS approach that simultaneously estimates the number of sources, separates the sources based on the sparseness of speech, estimates the direction of arrival of each source, and performs permutation alignment. We confirmed experimentally that reasonably...

The polynomial matrix EVD (PEVD) is an extension of the conventional eigenvalue decomposition (EVD) to polynomial matrices. The purpose of this article is to provide a review of the theoretical foundations of the PEVD and to highlight practical applications in the area of broadband blind source separation (BSS). Based on basic definitions of polynomial matrix terminology such as parahermitian a...