Maximum contrast analysis for nonnegative blind source separation

In this paper, we propose a maximum contrast analysis (MCA) method for nonnegative blind source separation, where both the mixing matrix and the source signals are nonnegative. We first show that the contrast degree of the source signals is greater than that of the mixed signals. Motivated by this observation, we propose an MCA-based cost function. It is further shown that the separation matrix can be obtained by maximizing the proposed cost function. Then we derive an iterative determinant maximization algorithm for estimating the separation matrix. In the case of two sources, a closed-form solution exists and is derived. Unlike most existing blind source separation methods, the proposed MCA method needs neither the independence assumption, nor the sparseness requirement of the sources. The effectiveness of the new method is illustrated by experiments using X-ray images, remote sensing images, infrared spectral images, and real-world fluorescence microscopy images.

Nonnegative blind source separation by sparse component analysis based on determinant measure

The problem of nonnegative blind source separation (NBSS) is addressed in this paper, where both the sources and the mixing matrix are nonnegative. Because many real-world signals are sparse, we deal with NBSS by sparse component analysis. First, a determinant-based sparseness measure, named D-measure, is introduced to gauge the temporal and spatial sparseness of signals. Based on this measure, a new NBSS model is derived, and an iterative sparseness maximization (ISM) approach is proposed to solve this model. In the ISM approach, the NBSS problem can be cast into row-to-row optimizations with respect to the unmixing matrix, and then the quadratic programming (QP) technique is used to optimize each row. Furthermore, we analyze the source identifiability and the computational complexity of the proposed ISM-QP method. The new method requires relatively weak conditions on the sources and the mixing matrix, has high computational efficiency, and is easy to implement. Simulation results demonstrate the effectiveness of our method.

Nonnegative Blind Source Separation by Sparse Component Analysis Based on Determinant Measure

The problem of nonnegative blind source separation (NBSS) is addressed in this paper, where both the sources and the mixing matrix are nonnegative. Because many real-world signals are sparse, we deal with NBSS by sparse component analysis. First, a determinant-based sparseness measure, named D-measure, is introduced to gauge the temporal and spatial sparseness of signals. Based on this measure, a new NBSS model is derived, and an iterative sparseness maximization (ISM) approach is proposed to solve this model. In the ISM approach, the NBSS problem can be cast into row-to-row optimizations with respect to the unmixing matrix, and then the quadratic programming (QP) technique is used to optimize each row. Furthermore, we analyze the source identifiability and the computational complexity of the proposed ISM-QP method. The new method requires relatively weak conditions on the sources and the mixing matrix, has high computational efficiency, and is easy to implement. Simulation results demonstrate the effectiveness of our method.

Blind Source Separation by Nonnegative Matrix Factorization with Minimum-Volume Constraint

Recently, nonnegative matrix factorization (NMF) attracts more and more attentions for the promising of wide applications. A problem that still remains is that, however, the factors resulted from it may not necessarily be realistically interpretable. Some constraints are usually added to the standard NMF to generate such interpretive results. In this paper, a minimum-volume constrained NMF is proposed and an efficient multiplicative update algorithm is developed based on the natural gradient optimization. The proposed method can be applied to the blind source separation (BSS) problem, a hot topic with many potential applications, especially if the sources are mutually dependent. Simulation results of BSS for images show the superiority of the proposed method.

Blind source separation by fully nonnegative constrained iterative volume maximization

Blind source separation (BSS) has been widely discussed in many real applications. Recently, under the assumption that both of the sources and the mixing matrix are nonnegative, Wang develop an amazing BSS method by using volume maximization. However, the algorithm that they have proposed can guarantee the nonnegativities of the sources only, but cannot obtain a nonnegative mixing matrix necessarily. In this letter, by introducing additional constraints, a method for fully nonnegative constrained iterative volume maximization (FNCIVM) is proposed. The result is with more interpretation, while the algorithm is based on solving a single linear programming problem. Numerical experiments with synthetic signals and real-world images are performed, which show the effectiveness of the proposed method.

Online blind source separation using incremental nonnegative matrix factorization with volume constraint

Online blind source separation (BSS) is proposed to overcome the high computational cost problem, which limits the practical applications of traditional batch BSS algorithms. However, the existing online BSS methods are mainly used to separate independent or uncorrelated sources. Recently, nonnegative matrix factorization (NMF) shows great potential to separate the correlative sources, where some constraints are often imposed to overcome the non-uniqueness of the factorization. In this paper, an incremental NMF with volume constraint is derived and utilized for solving online BSS. The volume constraint to the mixing matrix enhances the identifiability of the sources, while the incremental learning mode reduces the computational cost. The proposed method takes advantage of the natural gradient based multiplication updating rule, and it performs especially well in the recovery of dependent sources. Simulations in BSS for dual-energy X-ray images, online encrypted speech signals, and high correlative face images show the validity of the proposed method.

A convex geometry-based blind source separation method for separating nonnegative sources

This paper presents a convex geometry (CG)-based method for blind separation of nonnegative sources. First, the unaccessible source matrix is normalized to be column-sum-to-one by mapping the available observation matrix. Then, its zero-samples are found by searching the facets of the convex hull spanned by the mapped observations. Considering these zero-samples, a quadratic cost function with respect to each row of the unmixing matrix, together with a linear constraint in relation to the involved variables, is proposed. Upon which, an algorithm is presented to estimate the unmixing matrix by solving a classical convex optimization problem. Unlike the traditional blind source separation (BSS) methods, the CG-based method does not require the independence assumption, nor the uncorrelation assumption. Compared with the BSS methods that are specifically designed to distinguish between nonnegative sources, the proposed method requires a weaker sparsity condition. Provided simulation results illustrate the performance of our method.

An extension of slow feature analysis for nonlinear blind source separation

We present and test an extension of slow feature analysis as a novel approach to nonlinear blind source separation. The algorithm relies on temporal correlations and iteratively reconstructs a set of statistically independent sources from arbitrary nonlinear instantaneous mixtures. Simulations show that it is able to invert a complicated nonlinear mixture of two audio signals with a high reliability. The algorithm is based on a mathematical analysis of slow feature analysis for the case of input data that are generated from statistically independent sources. © 2014 Henning Sprekeler, Tiziano Zito and Laurenz Wiskott.

MISEP method for postnonlinear blind source separation

In this letter, a standard postnonlinear blind source separation algorithm is proposed, based on the MISEP method, which is widely used in linear and nonlinear independent component analysis. To best suit a wide class of postnonlinear mixtures, we adapt the MISEP method to incorporate a priori information of the mixtures. In particular, a group of three-layered perceptrons and a linear network are used as the unmixing system to separate sources in the postnonlinear mixtures, and another group of three-layered perceptron is used as the auxiliary network. The learning algorithm for the unmixing system is then obtained by maximizing the output entropy of the auxiliary network. The proposed method is applied to postnonlinear blind source separation of both simulation signals and real speech signals, and the experimental results demonstrate its effectiveness and efficiency in comparison with existing methods.

On the performance of a blind source separation based I/Q-corrector

I and Q Channel phase and gain mismatches are of great concern in communications receiver design. In this paper we carry out a detailed performance analysis of the Blind-Source Seperation (BSS) based imbalance compensation structure. The results indicate that the BSS structure can offer adequate performance for most communication systems. Since the compensation is carried out before any modulation specific processing, the proposed compensation method works with all standard modulation formats.

On the structure and performance of a novel blind source separation based carrier phase synchronization error compensator

In this paper we carry out a detailed performance analysis of a novel blind-source-seperation (BSS) based DSP algorithm that tackles the carrier phase synchronization error problem. The results indicate that the mismatch can be effectively compensated during the normal operation as well as in the rapidly changing environments. Since the compensation is carried out before any modulation specific processing, the proposed method works with all standard modulation formats and lends itself to efficient real-time custom integrated hardware or software implementations.