Blind source separation using second-order cyclostationary statistics

This paper studies the blind source separation (BSS) problem with the assumption that the source signals are cyclostationary. Identifiability and separability criteria based on second-order cyclostationary statistics (SOCS) alone are derived. The identifiability condition is used to define an appropriate contrast function. An iterative algorithm (ATH2) is derived to minimize this contrast function. This algorithm separates the sources even when they do not have distinct cycle frequencies .

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.

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.

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.

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.

Mixing vector construction for single channel semi-blind source separation using empirical mode decomposition

The Empirical Mode Decomposition (EMD) method is a commonly used method for solving the problem of single channel blind source separation (SCBSS) in signal processing. However, the mixing vector of SCBSS, which is the base of the EMD method, has not yet been effectively constructed. The mixing vector reflects the weights of original signal sources that form the single channel blind signal source. In this paper, we propose a novel method to construct a mixing vector for a single channel blind signal source to approximate the actual mixing vector in terms of keeping the same ratios between signal weights. The constructed mixing vector can be used to improve signal separations. Our method incorporates the adaptive filter, least square method, EMD method and signal source samples to construct the mixing vector. Experimental tests using audio signal evaluations were conducted and the results indicated that our method can improve the similar values of sources energy ratio from 0.2644 to 0.8366. This kind of recognition is very important in weak signal detection.