Bayesian separation of spectral sources under non-negativity and full additivity constraints

This paper addresses the problem of separating spectral sources which are linearly mixed with unknown proportions. The main difficulty of the problem is to ensure the full additivity (sum-to-one) of the mixing coefficients and non-negativity of sources and mixing coefficients. A Bayesian estimation approach based on Gamma priors was recently proposed to handle the non-negativity constraints in a linear mixture model. However, incorporating the full additivity constraint requires further developments. This paper studies a new hierarchical Bayesian model appropriate to the non-negativity and sum-to-one constraints associated to the regressors and regression coefficients of linear mixtures. The estimation of the unknown parameters of this model is performed using samples generated using an appropriate Gibbs sampler. The performance of the proposed algorithm is evaluated through simulation results conducted on synthetic mixture models. The proposed approach is also applied to the processing of multicomponent chemical mixtures resulting from Raman spectroscopy.Comment: v4: minor grammatical changes; Signal Processing, 200

A sparse semi-blind source identification method and its application to Raman spectroscopy for explosives detection

Rapid and reliable detection and identification of unknown chemical substances are critical to homeland security. It is challenging to identify chemical components from a wide range of explosives. There are two key steps involved. One is a non-destructive and informative spectroscopic technique for data acquisition. The other is an associated library of reference features along with a computational method for feature matching and meaningful detection within or beyond the library. In this paper, we develop a new iterative method to identify unknown substances from mixture samples of Raman spectroscopy. In the first step, a constrained least squares method decomposes the data into a sum of linear combination of the known components and a non-negative residual. In the second step, a sparse and convex blind source separation method extracts components geometrically from the residuals. Verification based on the library templates or expert knowledge helps to confirm these components. If necessary, the confirmed meaningful components are fed back into step one to refine the residual and then step two extracts possibly more hidden components. The two steps may be iterated until no more components can be identified. We illustrate the proposed method in processing a set of the so called swept wavelength optical resonant Raman spectroscopy experimental data by a satisfactory blind extraction of a priori unknown chemical explosives from mixture samples. We also test the method on nuclear magnetic resonance (NMR) spectra for chemical compounds identification. © 2013 Published by Elsevier B.V

Single channel speech music separation using nonnegative matrix factorization and spectral masks

A single channel speech-music separation algorithm based on nonnegative matrix factorization (NMF) with spectral masks is proposed in this work. The proposed algorithm uses training data of speech and music signals with nonnegative matrix factorization followed by masking to separate the mixed signal. In the training stage, NMF uses the training data to train a set of basis vectors for each source. These bases are trained using NMF in the magnitude spectrum domain. After observing the mixed signal, NMF is used to decompose its magnitude spectra into a linear combination of the trained bases for both sources. The decomposition results are used to build a mask, which explains the contribution of each source in the mixed signal. Experimental results show that using masks after NMF improves the separation process even when calculating NMF with fewer iterations, which yields a faster separation process

Learning the fundamental mid-infrared spectral components of galaxies with non-negative matrix factorization

The mid-infrared (MIR) spectra observed with the Spitzer Infrared Spectrograph (IRS) provide a valuable data set for untangling the physical processes and conditions within galaxies. This paper presents the first attempt to blindly learn fundamental spectral components of MIR galaxy spectra, using non-negative matrix factorization (NMF). NMF is a recently developed multivariate technique shown to be successful in blind source separation problems. Unlike the more popular multivariate analysis technique, principal component analysis, NMF imposes the condition that weights and spectral components are non-negative. This more closely resembles the physical process of emission in the MIR, resulting in physically intuitive components. By applying NMF to galaxy spectra in the Cornell Atlas of Spitzer/IRS sources, we find similar components amongst different NMF sets. These similar components include two for active galactic nucleus (AGN) emission and one for star formation. The first AGN component is dominated by fine structure emission lines and hot dust, the second by broad silicate emission at 10 and 18 μm. The star formation component contains all the polycyclic aromatic hydrocarbon features and molecular hydrogen lines. Other components include rising continuums at longer wavelengths, indicative of colder grey-body dust emission. We show an NMF set with seven components can reconstruct the general spectral shape of a wide variety of objects, though struggle to fit the varying strength of emission lines. We also show that the seven components can be used to separate out different types of objects. We model this separation with Gaussian mixtures modelling and use the result to provide a classification tool. We also show that the NMF components can be used to separate out the emission from AGN and star formation regions and define a new star formation/AGN diagnostic which is consistent with all MIR diagnostics already in use but has the advantage that it can be applied to MIR spectra with low signal-to-noise ratio or with limited spectral range. The seven NMF components and code for classification are available at https://github.com/pdh21/NMF_software/