Given a set of mixtures, blind source separation attempts to retrieve the source signals without or with very little information of the mixing process. We present a geometric approach for blind separation of nonnegative linear mixtures termed <i>facet component analysis</i>. The approach is based on facet identification of the underlying cone structure of the data. Earlier works focus on recovering the cone by locating its vertices (vertex component analysis) based on a mutual sparsity condition which requires each source signal to possess a stand-alone peak in its spectrum. We formulate alternative conditions so that enough data points fall on the facets of a cone instead of accumulating around the vertices. To find a regime of unique solvability, we make use of both geometric and density properties of the data points and develop an efficient facet identification method by combining data classification and linear

Motivated by the nuclear magnetic resonance (NMR) spectroscopy of biofluids (urine and blood serum), we present a recursive blind source separation (rBSS) method for nonnegative and correlated data. BSS problem arises when one attempts to recover a set of source signals from a set of mixture signals without knowing the mixing process. Various approaches have been developed to solve BSS problems relying on the assumption of statistical independence of the source signals. However, signal independence is not guaranteed in many real-world data like the NMR spectra of chemical compounds. The rBSS method introduced in this paper deals with the nonnegative and correlated signals arising in NMR spectroscopy of biofluids. The statistical independence requirement is replaced by a constraint which requires dominant interval(s) from each source signal over some of the other source signals in a

Motivated by applications in nuclear magnetic resonance (NMR) spectroscopy, we introduce a novel blind source separation (BSS) approach to treat nonnegative and correlated data. We consider the (over)-determined case where n sources are to be separated from n linear mixtures (n). Among the n source signals, there are n partially overlapping (Po) sources and one positive everywhere (Pe) source. This condition is applicable for many real-world signals such as NMR spectra of urine and blood serum for metabolic fingerprinting and disease diagnosis. The geometric properties of the mixture matrix and the sparseness structure of the source signals (in a transformed domain) are crucial to the identification of the mixing matrix and the sources. The method first identifies the mixing coefficients of the Pe source by exploiting geometry in data clustering. Then subsequent elimination of variables leads to a sub

A convex speech enhancement (CSE) method is presented based on convex optimization and pause detection of the speech sources. Channel spatial difference is identified for enhancing each speech source individually while suppressing other interfering sources. Sparse unmixing filters indicating channel spatial differences are sought by <i>l</i> ₁ norm regularization and the split Bregman method. A subdivided split Bregman method is developed for efficiently solving the problem in severely reverberant environments. The speech pause detection is based on a binary mask source separation method. The CSE method is evaluated objectively and subjectively, and found to outperform a list of existing blind speech separation approaches on both synthetic and room recorded speech mixtures in terms of the overall computational speed and separation quality.

We study an efficient dynamic blind source separation algorithm of convolutive sound mixtures based on updating statistical information in the frequency domain, and minimizing the support of time domain demixing filters by a weighted least square method. The permutation and scaling indeterminacies of separation, and concatenations of signals in adjacent time frames are resolved with optimization of l 1 l norm on cross-correlation coefficients at multiple time lags. The algorithm is a direct method without iterations, and is adaptive to the environment. Computations on recorded benchmark mixtures of speech and music signals show excellent performance. The method in general separates a foreground source from a background of sounds as often encountered in realistic situations.