Multi-channel high resolution blind image restoration

Multiframe super-resolution is the problem of reconstructing a single high-resolution (HR) image from several low-resolution (LR) versions of it. We assume that the original HR image undergoes different linear transforms, where each transform can be approximated as a set of linear shift-invariant transforms over different subregions of the HR image. The linearly transformed versions of the HR image are then downsampled, resulting in different LR images. Under the assumption of linearity, these LR images can form a basis that spans the set of the polyphase components (PPCs) of the HR image. We propose sampling rate diversity, where a secondary LR image, acquired by a secondary sensor of different (lower) sampling rate, is used as a reference to make known portions (subpolyphase components) of the PPCs of the reconstructed HR image. This setup allows for non-parametric reconstruction of the PPCs, where no knowledge of the underlying transforms is required, by solving for the expansion coefficients of the PPCs, in terms of the LR basis.

Blind Signal Separation II. Linear, Convolutive Combinations: II. Linear, Convolutive Combinations

Most of the existing algorithms for blind sources separation have a limitation that sources are statistically independent. However, in many practical applications, the source signals are nonnegative and mutual statistically dependent signals. When the observations are nonnegative linear combinations of nonnegative sources, the correlation coefficients of the observations are larger than these of source signals. In this letter, a novel Nonnegative Matrix Factorization (NMF) algorithm with least correlated component constraints to blind separation of convolutive mixed sources is proposed. The algorithm relaxes the source independence assumption and has low-complexity algebraic computations. Simulation results on blind source separation including real face image data indicate that the sources can be successfully recovered with the algorithm.

Blind source separation (BSS) consists in processing a set of observed mixed signals to separate them into a set of original components. Most of the current blind separation methods assumes that the source signals are “as statistically independent as possible” given the observed data. In many real-world situations, however, this hypothesis does not hold. In order to cope with such signals, a first geometric method was proposed that separates statistically dependent signals, provided that they are nonnegative and locally orthogonal.This paper presents a new geometric method for the separation of nonnegative source signals which relies on a working assumption that is weaker than local orthogonality. The separation problem is expressed as the identification of relevant facets of the data cone. After a rigorous proof of the proposed method, the details of the separation algorithm are given. Experiments on signals from various origins clearly show the efficiency of the new procedure.

We present a new approach to independent component analysis (ICA) by extending the formulation of univariate source signals to multivariate source signals. The new approach is termed independent vector analysis (IVA). In the model, we assume that linear mixing model exists in each dimension separately, and the latent sources are independent of the others. In contrast to ICA, the sources are random vectors, not just single variables, which means the elements of a random vector are closely related to the others. Thus, we assume the dependency between the elements of a source vector. In this manner, we define dependence between vectors as Kullback-Leibler divergence between the total joint probability of vectors and the product of marginal probabilities of vectors. Then, the model allows independence between multivariate source signals represented as random vectors, and dependence between the source signals within the vector representation. The proposed vector density model can for example capture variance dependencies within a vector source signal. There are several applications of this new formulation. In the separation of acoustic sources, the algorithm mitigates the permutation problem, i.e. the usual ICA algorithms applied in to the frequency domain mixture data suffer from the unknown permutation of the output signals. Although there are several engineering solutions to fix this problem after the ICA stage, the proposed method provides a natural solution to the problem by capturing the inherent dependencies of the acoustic signals. It therefore avoids the permutation problem and allows the separation of sources in very challenging environments for many sound sources.

We present a simple efficient local unsupervised learning algorithm for online adaptive multichannel blind deconvolution and separation of i.i.d. sources. Under mild conditions, there exits a stable inverse system so that the source signals can be exactly recovered from their convolutive mixtures. Based on the existence of the inverse filter, we construct a two-stage neural network which consists of blind equalization and source separation. In the blind equalization stage, we employ anti-Hebbian learning in the temporal domain for decorrelation. For blind separation, we can apply any existing algorithms. Extensive computer simulations confirm the validity and high performance of our proposed learning algorithm.

Blind separation for dependent sources and multi-Gaussian sources is a challenging problem. This letter proposes a new adaptive blind source separation algorithm, which is referred to as vector auto-regressive diagonalization (VAR-JD), to deal with this problem. This algorithm estimates demixing matrix by matrix joint JD of a set of matrices containing the estimated VAR coefficients. Compared with traditional adaptive BSS method, which assumes that source signals are mutual independent and no more than one Gaussian source signal exists, the proposed VAR-JD algorithm is not only able to separate independent source signals but also dependent source signals, and there is no demand for the number of Gaussian source signals. Simulation results on the separation of synthetic and communication signals demonstrate the effectiveness of the proposed approach. This latter is important to anti-jamming communications. Moreover, VAR-JD is suitable for determined mixtures and can extend easily to overdetermined mixtures.

Blind separation of non-stationary sources using continuous density hidden Markov models

In the case of multiple nonstationary independent source signals and linear instantaneous time-varying mixing systems, it is difficult to adaptively separate the multiple source signals. Therefore, the adaptive blind source separation (BSS) problem is firstly formally expressed and compared with tradition BSS problem. Then, we propose an adaptive blind identification and separation method based on the variable learning rate equivariant adaptive source separation via independence (EASI) algorithm. Furthermore, we analyze the scope and conditions of variable-learning rate EASI algorithm. The adaptive BSS simulation results also show that the variable learning rate EASI algorithm provides better separation effect than the fixed learning rate EASI and recursive least-squares algorithms.

In order to overcome the problem of low accuracy and poor stability caused by the one-sided information blind separation analysis of the current communication channel interference suppression research methods, this paper proposes the optical communication network channel interference suppression method based on blind signal separation algorithm. The receiver unit, field programmable gate array (FPGA) unit, memory chip group and other modules are used to construct the channel signal acquisition system, and the collected signals are preprocessed by centralisation and whitening. Based on the signal preprocessing results, the blind separation of instantaneous linear mixed signals, blind separation of convolutional mixed signals and blind separation of sparse sources were comprehensively analysed to obtain the source signals and realise channel interference suppression of optical communication network. Experimental results show that this method has high interference precision, strong stability and good application prospect.

A novel blind separation approach using higher-order time-frequency distributions is presented. The concept of higher-order time-frequency distribution matrix is also introduced. It is devised to primarily separate sources with temporal nonstationary signal characteristics. So far, this problem has been solved using statistical information available on the source signals. In contrast to well known blind source separation approaches using second-order statistics (SOS) and/or higher-order statistics (HOS) which rely on stationarity properties of the signals, the proposed approach allows separation of the sources with nonstationarity properties. In addition, the effect of spreading the noise power while localizing of the source energy in the time-frequency domain amounts to increasing the signal to noise ratio. A computationally feasible implementation is presented based on joint diagonalization of the matrices of the principal slices of the time-multifrequency domain of support of the cumulant-based Wigner trispectrums. Numerical examples demonstrate the effectiveness of the proposed approach.

We presents a new necessary and sufficient condition for the blind separation of sources having non-zero kurtosis, from their linear mixtures. It is shown here that a new blind separation criterion based on both odd (f(y)=y/sup 3/) and even (f(y)=y/sup 2/) functions, presents desirable solutions, provided that all source signals have negative kurtosis (sub-Gaussian) or have positive kurtosis (super-Gaussian). Based on this new separation criterion, a linear feedforward network with lateral feedback connections is constructed. Both theoretical and computer simulation results are presented.

A sequential algorithm for the blind separation of a class of periodic source signals is introduced in this paper. The algorithm is based only on second-order statistical information and exploits the assumption that the source signals have distinct periods. Separation is performed by sequentially converging to a solution which in effect diagonalizes the output covariance matrix constructed at a lag corresponding to the fundamental period of the source we select, the one with the smallest period. Simulation results for synthetic signals and real electrocardiogram recordings show that the proposed algorithm has the ability to restore statistical independence, and its performance is comparable to that of the equivariant adaptive source separation (EASI) algorithm, a benchmark high-order statistics-based sequential algorithm with similar computational complexity. The proposed algorithm is also shown to mitigate the limitation that the EASI algorithm can separate at most one Gaussian distributed source. Furthermore, the steady-state performance of the proposed algorithm is compared with that of EASI and the block-based second-order blind identification (SOBI) method.

Most of the HO blind source separation methods developed this last decade aim at blindly separating statistically independent sources, assumed stationary and ergodic. Nevertheless, in many situations such as in radiocommunications, the sources are non-stationary and very often (quasi)-cyclostationary (digital modulations). In these contexts, it is important to wonder if the performance of these HO blind source separation methods may be affected by the potential non-stationarity of the sources. The purpose of this paper is to bring some answers to this question through the behaviour analysis of the empirical fourth-order cumulant estimators in the presence of (quasi)-cyclostationary sources.

The methods that can be done for the estimation of the number of source signals and separation of source signals using time‐frequency information are proposed as a method of blind source separation. In these methods, some independent conditions are assumed in a time‐frequency domain, and observed signals are expanded to time‐frequency domain using wavelet analysis. However, these methods are not considered phase differences (difference of distance) between source signals and observed signals. A new method is proposed. The method can be done not only for the source separation but also the specification of the locations of source signals considering phase differences. In this method, it is necessary to assume a rather stronger independent condition than former methods. But, on account of this assumption, a function that becomes a real value only when phase differences are coincidence in time‐frequency domain is determined. Using this function, first of all, the number of source signals is calculated, then the locations of source signals and source signals are calculated. The effectiveness of the method is shown using actual synthetic signals.