This work deals with the estimation fusion for distributed multisensor systems under the framework of local estimates being taken as probability density functions. The estimation fusion is formulated to an optimization problem that minimizes the sum of squared distances between the fused probability density and each local probability density. The maximum mean discrepancy, which is a distance between two probability density functions, is considered. It is defined by the kernel mean embeddings from the probability density function space to a reproducing kernel Hilbert space. For the quadratic, cubic and Gaussian kernels, either the analytical solutions are derived or the numerical methods are developed for solving the aforementioned optimization problem. Numerical experiments are provided to illustrate the performance of the proposed estimation fusion methods.

Fusing a hyperspectral image (HSI) and a multispectral image (MSI) to generate a super-resolution image (SRI) with refined spatial and spectral resolution is a popular technique in hyperspectral super-resolution (HSR). Most HSR methods accomplish this task by matrix or tensor decomposition in the framework of linear unmixing. Although these methods are effective to some extent, serious challenges remain. In this work, the linear unmixing is extended to nonlinear unmixing framework and a novel HSR method based on a generalized bilinear unmixing model in tensor format is proposed. Apart from the linear part, it additionally considers bilinear interactions between endmembers. A low-rank prior is incorporated into the abundance maps and nonlinear interaction abundance maps, which can adequately model non-local similarities in images. In addition, the total variance is used to explore the local spatial relationships of the image. The optimization is implemented using the alternating direction method of multipliers (ADMM) algorithm with analytical expressions for each iterative update step, which is difficult to implement even for algorithms that focus on nonlinear unmixing. The proposed method overcomes the inherent linear limitations of the linear unmixing framework and avoids the information loss caused by matrixing the HSI and MSI with 3D-structure. The experimental results of simulations on real hyperspectral datasets demonstrate the superiority of the proposed approach over the compared HSR methods.

Sub-pixel target detection is a challenging task in hyperspectral image processing. Most statistical detectors rely on the estimation of the background covariance matrix. In contrast to the traditional approaches by adopting global covariance matrix estimation from all image pixels, the local estimation within image segments can significantly improve detection performance for complex backgrounds in many scenarios. However, the local covariance matrix estimate may be unstable due to the high spectral dimension of the hyperspectral image, especially when the size of the local sample representing background pixels, is relatively small. In this work, a random projection (RP) is employed to reduce the spectral dimension, and a spectral similarity-based dual-window (SSDW) strategy is suggested to appropriately extract the local background statistical properties. So, a kind of sub-pixel target detector is developed in a statistical hypothesis testing framework for different observation models under t-distribution background. Especially, the projection dimension is determined without any extra experiment or training and ensures asymptotic optimality of detection power under some conditions. The superior performance of the proposed detectors is demonstrated by some synthetic data and real hyperspectral images.

Graph embedding (GE) provides an effective way to reveal the intrinsic feature of high-dimensional data on the foundation of preserving topological properties. Under the framework of GE, the hyperspectral image can be represented by a weighted graph, where pixels and similarities among them are treated as vertices and edge weights, respectively. In this article, an adaptive reference-related GE (ARGE) method is proposed to efficaciously obtain the low-dimensional feature and improve computational efficiency. The ARGE method is composed of two primary processes. The key to connecting these two processes is the reference vertices set, which is the abstraction of graph topological features. First, the reference vertices are adaptively selected through a three-step adaptive reference set selection (ARSS) algorithm. Second, the original high-dimensional graph is embedded as a low-dimensional graph through preserving the reference-related structure. Specifically, the pairwise similarities between vertices and reference vertices are preserved in embedding space. In addition, a new hybrid dissimilarity measure of Rao distance and spectral information divergence (RD-SID) is designed to depict the spectral difference between pixels. To evaluate the effectiveness of the proposed method, the obtained low-dimensional feature is fed into the anomaly detector to detect anomalous pixels. The experimental results on five real and one synthetic hyperspectral datasets demonstrate the superiority of the proposed ARGE method over the compared feature extraction methods.

This letter deals with Gaussian approximation of complicated posterior distribution involved in the Bayesian paradigm for nonlinear dynamic systems. A general formulation for Gaussian approximation is first provided by equivalently representing posterior distribution as a Gaussian one with some constraint via embedding technique. In this work, it is specified as a penalized Kullback–Leibler divergence minimization problem. This minimization is solved for the expected Gaussian approximation by utilizing a pre-selected cubature rule and the conditional gradient method. Then, a novel iterative filter is developed for nonlinear dynamic systems. In addition, it is also proved to be optimal in linear cases and demonstrated to be effective through simulations.

This letter deals with similarity parameter selection for knowledge-aided covariance matrix estimation in adaptive radar signal processing. Starting from the observation that the maximum likelihood estimate of the interference covariance matrix under a similarity constraint admits a closed-form expression, which depends on the similarity parameter, an adaptive procedure is devised to get a parameter free estimator. The technique is based on the expected likelihood principle and requires the solution of an implicit equation, which can be efficiently pursued via the bisection method due a monotonicity property. The analysis of the estimator, conducted also in comparison with the counterpart based on the cross-validation method confirms its effectiveness in terms of both performance and computational complexity.

The problem of detecting unknown signals using the observations received from an array system with or without perfectly calibrated sensors is addressed. It is formulated as a statistical hypothesis testing on the covariance structure of the received signal. For the received signals following the elliptically symmetric distributions, the generalized likelihood ratio test (GLRT) statistics are derived. Specially, the GLRT detectors for uniform linear arrays are provided. Numerical experiments show the effectiveness of the proposed detectors.

In this paper, an improved shrinkage-to-tapering oracle approximating approach for estimating high-dimensional covariance matrices is proposed. Since the oracle shrinkage coefficient of shrinkage-to-tapering oracle (STO) estimator is greater than one for some tapering parameter, the optimal shrinkage coefficient is obtained by thresholding the oracle coefficients. The corresponding normalized mean-squared error (MSE) is also obtained. Moreover, an improved shrinkage-to-tapering estimator is proposed by plugging the unbiased and consistent estimators of some functions of unknown covariance matrix into the optimal coefficient and corresponding normalized MSE. Compared with the STO approximating approach using iteration to approximate the oracle coefficient, a closed-form formula of the estimated coefficient and the normalized MSE are derived for given tapering parameter. Numerical simulations and an application to adaptive beamforming show the comparable performance of the proposed estimator.

In the multiple target tracking scenarios, the correct matching between targets and measurements is critical. There have been many approaches to resolve this problem called data association. In this paper, a regression method is proposed to resolve the data association problem. In the logistic regression model, nine potential predictor variables are designed which are related to the geometric information of measurements and estimated states of multiple targets, including the distance, intersection angle of position vectors and smoothness of tracks at current time instant and several previous time steps, and the dependent variable is the association probability of matching the measurement with all targets. The regression coefficients are trained through a designed multiple target tracking system. For the new unknown tracking systems with the given number of tracked targets, the measurement having the highest association probability with a target is considered as the true measurement about such target using the trained empirical regression model. Moreover, various filtering algorithms can be invoked to tracking targets. Simulation studies show the proposed novel mechanism for tackling with data association problem in multiple target tracking is effective.

This paper addresses the shrinkage estimation problem of high-dimensional covariance matrices with low sample size data. A class of structured target matrices that include banding, thresholding, diagonal and block diagonal matrices is proposed, and an optimal oracle shrinkage coefficient is derived. To approximate the oracle estimator, an iterative method is presented and proved to be convergent. Moreover, a closed-form solution of its limit, which is guaranteed to be in the unit interval, is obtained. For the banding and thresholding target matrices with unknown bandwidth and threshold respectively, two adaptive algorithms are presented to estimate the covariance matrix, and some properties on the estimation error are discussed theoretically. Some simulations are given to illustrate the competitive performances of proposed covariance matrix estimators.

In this paper, the robust estimation fusion problem in multisensor systems with norm-bounded uncertainties concerning the error covariance matrix between local estimates is addressed. A robust fusion method by minimizing the worst-case fused mean-squared error (MSE) for all feasible error covariance matrices of local estimates is proposed. The minimax robust fusion weighting matrices can be explicitly formulated as a function of solution of a semidefinite programming (SDP). Some numerical examples demonstrate that when the error covariance matrix suffers disturbance, the proposed fusion method is more robust than the nominal fusion method which ignores the uncertainties, and can improve the performance when the disturbance is considerably large.

In this paper, the communication direction problem of a two-sensor tandem binary decision system is considered. Rigorous analysis shows that the performance of communication from the sensor with higher noise power to the sensor with lower noise power is not always better than the performance of the reverse communication direction when the signal and sensor noises are both Gaussian. This result can be extended to a more general two-sensor tandem binary decision system without the assumption of a specific data distribution. This seems somewhat counterintuitive but has significance for optimization design of sensor communication direction. Computer experiments support our analytic results and illustrate interesting information which requires need further study.

Under the assumption of independent observation noises across sensors, Bar-Shalom and Campo proposed a distributed fusion formula for two-sensor systems, whose main calculation is the inverse of submatrices of the error covariance of two local estimates instead of the inverse of the error covariance itself. However, the corresponding simple estimation fusion formula is absent in a general distributed multisensor system. In this paper, an efficient iterative algorithm for distributed multisensor estimation fusion without any restrictive assumption on the noise covariance (i.e., the assumption of independent observation noises across sensors and the two-sensor system, and the direct computation of the Moore-Penrose generalized inverse of the joint error covariance of local estimates are not necessary) is presented. At each iteration, only the inverse or generalized inverse of a matrix having the same dimension as the error covariance of a single-sensor estimate is required. In fact, the proposed algorithm is a generalization of Bar-Shalom and Campo's fusion formula and reduces the computational complexity significantly since the number of iterative steps is less than the number of sensors. An example of a three-sensor system shows how to implement the specific iterative steps and reduce the computational complexities

Page segmentation is one of the important and basic research subjects of document analysis. There are two major kinds of page segmentation methods, i.e. hierarchical and no-hierarchical ones. Most traditional techniques such as top–down and bottom–up approaches belong to the hierarchical method. Though these two approaches have been used till now, they are not effective for processing documents with high geometric complexity and the process of splitting document needs iterative operations which is time consuming. A non-hierarchical method called the modified fractal signature (MFS) was presented in recent years. It can overcome the above weaknesses, however the MFS needs to calculate modified fractal signature which makes the theory very complex. In this thesis, we present a new page segmentation approach: Median Order Statistic Filter (MedOSF) — Maximum Order Statistic Filter (MaxOSF) approach which is more direct and much simpler. We use the MedOSF to remove the salt–pepper noise of the document and use the MaxOSF to do the page segmentation. In practice, they not only can adaptively process the documents with high geometrical complexity, but also save a lot of computing time.