Novel Z-Domain precoding method for blind separation of spatially correlated signals

In this paper, we address the problem of blind separation of spatially correlated signals, which is encountered in some emerging applications, e.g., distributed wireless sensor networks and wireless surveillance systems. We preprocess the source signals in transmitters prior to transmission. Specifically, the source signals are first filtered by a set of properly designed precoders and then the coded signals are transmitted. On the receiving side, the Z-domain features of the precoders are exploited to separate the coded signals, from which the source signals are recovered. Based on the proposed precoders, a closed-form algorithm is derived to estimate the coded signals and the source signals. Unlike traditional blind source separation approaches, the proposed method does not require the source signals to be uncorrelated, sparse, or nonnegative. Compared with the existing precoder-based approach, the new method uses precoders with much lower order, which reduces the delay in data transmission and is easier to implement in practice.

Projection-pursuit-based method for blind separation of nonnegative sources

This paper presents a projection pursuit (PP) based method for blind separation of nonnegative sources. First, the available observation matrix is mapped to construct a new mixing model, in which the inaccessible source matrix is normalized to be column-sum-to-1. Then, the PP method is proposed to solve this new model, where the mixing matrix is estimated column by column through tracing the projections to the mapped observations in specified directions, which leads to the recovery of the sources. The proposed method is much faster than Chan's method, which has similar assumptions to ours, due to the usage of optimal projection. It is also more advantageous in separating cross-correlated sources than the independence- and uncorrelation-based methods, as it does not employ any statistical information of the sources. Furthermore, the new method does not require the mixing matrix to be nonnegative. Simulation results demonstrate the superior performance of our method.

Separation of Doppler radar-based respiratory signatures

Respiration detection using microwave Doppler radar has attracted significant interest primarily due to its unobtrusive form of measurement. With less preparation in comparison with attaching physical sensors on the body or wearing special clothing, Doppler radar for respiration detection and monitoring is particularly useful for long-term monitoring applications such as sleep studies (i.e. sleep apnoea, SIDS). However, motion artefacts and interference from multiple sources limit the widespread use and the scope of potential applications of this technique. Utilising the recent advances in independent component analysis (ICA) and multiple antenna configuration schemes, this work investigates the feasibility of decomposing respiratory signatures into each subject from the Doppler-based measurements. Experimental results demonstrated that FastICA is capable of separating two distinct respiratory signatures from two subjects adjacent to each other even in the presence of apnoea. In each test scenario, the separated respiratory patterns correlate closely to the reference respiration strap readings. The effectiveness of FastICA in dealing with the mixed Doppler radar respiration signals confirms its applicability in healthcare applications, especially in long-term home-based monitoring as it usually involves at least two people in the same environment (i.e. two people sleeping next to each other). Further, the use of FastICA to separate involuntary movements such as the arm swing from the respiratory signatures of a single subject was explored in a multiple antenna environment. The separated respiratory signal indeed demonstrated a high correlation with the measurements made by a respiratory strap used currently in clinical settings.

Motion artefact separation in single channel doppler radar respiration measurement

Direct conversion Doppler radar has the capability to remotely monitor human respiratory activity in a non-contact form. However, the motion or movement from the subject will degrade the acquired respiration signal. As the respiration pattern is one of the essential parameters in respiratory medicine intrinsically containing more information about the respiratory function, it is particularly important to suppress or to separate these motion artefacts in order to reconstruct the corresponding patterns. Experiment results show that EMD-ICA algorithm is capable of separating the mixed respiration signal by recovering the useful information of the breathing pattern as well as the motion signatures using only a single channel measurement when using the source separation algorithm. This reduces the complexity and the cost of the sensing system while removing the undesirable artefacts. A high correlation was also observed from the recovered respiration pattern in comparison to the standard respiration strap for both experiments setup (a seated and a supine position).

A novel monotonic fixed-point algorithm for l1-regularized least square vector and matrix problem

Least square problem with l₁ regularization has been proposed as a promising method for sparse signal reconstruction (e.g., basis pursuit de-noising and compressed sensing) and feature selection (e.g., the Lasso algorithm) in signal processing, statistics, and related fields. These problems can be cast as l₁-regularized least-square program (LSP). In this paper, we propose a novel monotonic fixed point method to solve large-scale l₁-regularized LSP. And we also prove the stability and convergence of the proposed method. Furthermore we generalize this method to least square matrix problem and apply it in nonnegative matrix factorization (NMF). The method is illustrated on sparse signal reconstruction, partner recognition and blind source separation problems, and the method tends to convergent faster and sparser than other l₁-regularized algorithms.

Sparse Representations of Image via Overcomplete Dictionary Learned by Adaptive Non-orthogonal Sparsifying Transform

How to learn an over complete dictionary for sparse representations of image is an important topic in machine learning, sparse coding, blind source separation, etc. The so-called K-singular value decomposition (K-SVD) method [3] is powerful for this purpose, however, it is too time-consuming to apply. Recently, an adaptive orthogonal sparsifying transform (AOST) method has been developed to learn the dictionary that is faster. However, the corresponding coefficient matrix may not be as sparse as that of K-SVD. For solving this problem, in this paper, a non-orthogonal iterative match method is proposed to learn the dictionary. By using the approach of sequentially extracting columns of the stacked image blocks, the non-orthogonal atoms of the dictionary are learned adaptively, and the resultant coefficient matrix is sparser. Experiment results show that the proposed method can yield effective dictionaries and the resulting image representation is sparser than AOST.

Nonorthogonal approximate joint diagonalization with well-conditioned diagonalizers

To make the results reasonable, existing joint diagonalization algorithms have imposed a variety of constraints on diagonalizers. Actually, those constraints can be imposed uniformly by minimizing the condition number of diagonalizers. Motivated by this, the approximate joint diagonalization problem is reviewed as a multiobjective optimization problem for the first time. Based on this, a new algorithm for nonorthogonal joint diagonalization is developed. The new algorithm yields diagonalizers which not only minimize the diagonalization error but also have as small condition numbers as possible. Meanwhile, degenerate solutions are avoided strictly. Besides, the new algorithm imposes few restrictions on the target set of matrices to be diagonalized, which makes it widely applicable. Primary results on convergence are presented and we also show that, for exactly jointly diagonalizable sets, no local minima exist and the solutions are unique under mild conditions. Extensive numerical simulations illustrate the performance of the algorithm and provide comparison with other leading diagonalization methods. The practical use of our algorithm is shown for blind source separation (BSS) problems, especially when ill-conditioned mixing matrices are involved.

Nonnegative Matrix Factorization Applied to Nonlinear Speech and Image Cryptosystems

Nonnegative matrix factorization (NMF) is widely used in signal separation and image compression. Motivated by its successful applications, we propose a new cryptosystem based on NMF, where the nonlinear mixing (NLM) model with a strong noise is introduced for encryption and NMF is used for decryption. The security of the cryptosystem relies on following two facts: 1) the constructed multivariable nonlinear function is not invertible; 2) the process of NMF is unilateral, if the inverse matrix of the constructed linear mixing matrix is not nonnegative. Comparing with Lin's method (2006) that is a theoretical scheme using one-time padding in the cryptosystem, our cipher can be used repeatedly for the practical request, i.e., multitme padding is used in our cryptosystem. Also, there is no restriction on statistical characteristics of the ciphers and the plaintexts. Thus, more signals can be processed (successfully encrypted and decrypted), no matter they are correlative, sparse, or Gaussian. Furthermore, instead of the number of zero-crossing-based method that is often unstable in encryption and decryption, an improved method based on the kurtosis of the signals is introduced to solve permutation ambiguities in waveform reconstruction. Simulations are given to illustrate security and availability of our cryptosystem.

Mixing Matrix Estimation From Sparse Mixtures With Unknown Number of Sources

In blind source separation, many methods have been proposed to estimate the mixing matrix by exploiting sparsity. However, they often need to know the source number a priori, which is very inconvenient in practice. In this paper, a new method, namely nonlinear projection and column masking (NPCM), is proposed to estimate the mixing matrix. A major advantage of NPCM is that it does not need any knowledge of the source number. In NPCM, the objective function is based on a nonlinear projection and its maxima just correspond to the columns of the mixing matrix. Thus a column can be estimated first by locating a maximum and then deflated by a masking operation. This procedure is repeated until the evaluation of the objective function decreases to zero dramatically. Thus the mixing matrix and the number of sources are estimated simultaneously. Because the masking procedure may result in some small and useless local maxima, particle swarm optimization (PSO) is introduced to optimize the objective function. Feasibility and efficiency of PSO are also discussed. Comparative experimental results show the efficiency of NPCM, especially in the cases where the number of sources is unknown and the sources are relatively less sparse.

Blind extraction of cyclostationary signal from convolutional mixtures

Extracting a signal of interest from available measurements is a challenging problem. One property which can be utilized to extract the signal is cyclostationarity, which exists in many signals. Various blind source separation methods based on cyclostationarity have been reported in the literature but they assume that the mixing system is instantaneous. In this paper, we propose a method for blind extraction of cyclostationary signal from convolutional mixtures. Given that the signal of interest has a unique cyclostationary frequency and the sensors are placed close to the concerned signal, we show that the signal of interest can be estimated from the measured data. Simulations results show the effectiveness of our method.

Blind estimation of MIMO relay channels

In this paper, we integrate two blind source separation (BSS) methods to estimate the individual channel state information (CSI) for the source-relay and relay-destination links of three-node two-hop multiple-input multiple-output (MIMO) relay systems. In particular, we propose a first-order Z-domain precoding technique for the blind estimation of the relay-destination channel matrix, while an algorithm based on the constant modulus and mutual information properties is developed to estimate the source-relay channel matrix. Compared with training-based MIMO relay channel estimation approaches, our algorithm has a better bandwidth efficiency as no bandwidth is wasted for sending the training sequences. Numerical examples are shown to demonstrate the performance of the proposed algorithm. © 2014 IEEE.