Recent work has shown that existing powerful Bayesian hyperspectral unmixing algorithms can be significantly improved by incorporating the inherent local spatial correlations between pixel class labels via the use of Markov random fields. We here propose a new Bayesian approach to joint hyperspectral unmixing and image classification such that the previous assumption of stochastic abundance vectors is relaxed to a formulation whereby a common abundance vector is assumed for pixels in each class. This allows us to avoid stochastic reparameterizations and, instead, we propose a symmetric Dirichlet distributionmodel with adjustable parameters for the common abundance vector of each class. Inference over the proposed model is achieved via a hybrid Gibbs sampler, and in particular, simulated annealing is introduced for the label estimation in order to avoid the local-trap problem. Experiments on a synthetic image and a popular, publicly available real data set indicate the proposed model is faster than and outperforms the existing approach quantitatively and qualitatively. Moreover, for appropriate choices of the Dirichlet parameter, it is shown that the proposed approach has the capability to induce sparsity in the inferred abundance vectors. It is demonstrated that this offers increased robustness in cases where the preprocessing endmember extraction algorithms overestimate the number of active endmembers present in a given scene.

The robust principal component analysis (PCA) method has shown very promising results in seismic ambient noise attenuation when dealing with outliers in the data. However, the model assumes a general Gaussian distribution plus sparse outliers for the noise. In seismic data however, the noise standard variation could vary from one place to another leading to a more heavy-tailed noise distribution. In this paper, we present a new method which solves a convex minimisation problem of the robust PCA method with an M-estimate penalty function. Our empirical results show that the proposed method can outperform the robust PCA method.

This paper reconciles Kingsbury's dual-tree complex wavelets with Nason and Eckley's locally stationary model. We here establish that the dual-tree wavelets admit an invertible de-biasing matrix and that this matrix can be used to invert the covariance relation. We also show that the added directional selectivity of the proposed model adds utility to the standard two-dimensional local stationary model. Non-stationarity detection on random fields is used as a motivating example. Experiments confirm that the dual-tree model can distinguish anisotropic non-stationarities significantly better than the current model.

We here combine the rich, overcomplete signal representation afforded by the scattering transform together with a probabilistic graphical model which captures hierarchical dependencies between coefficients at different layers. The wavelet scattering network result in a high-dimensional representation which is translation invariant and stable to deformations whilst preserving informative content. Such properties are achieved by cascading wavelet transform convolutions with non-linear modulus and averaging operators. The network structure and its distributions are described using a Hidden Markov Tree. This yields a generative model for high-dimensional inference and offers a means to perform various inference tasks such as prediction. Our proposed scattering convolutional hidden Markov tree displays promising results on classification tasks of complex images in the challenging case where the number of training examples is extremely small.

We here establish and exploit the result that 2D isotropic self-similar fields beget quasi-decorrelated wavelet coefficients and that the resulting localised log sample second moment statistic is asymptotically normal. This leads to the development of a semi-local scaling exponent estimation framework with optimally modified weights. Furthermore, recent interest in penalty methods for least square problems and generalized Lasso for scaling exponent estimation inspires the simultaneous incorporation of both bounding box constraints and total variation smoothing into an iteratively reweighted least-square estimator framework. Numerical results on fractional Brownian fields with global and piecewise constant, semi-local Hurst parameters illustrate the benefits of the new estimators.

Recent work in off-line Reinforcement Learning has focused on efficient algorithms to incorporate feature selection, via l1-regularization, into the Bellman operator fixed-point estimators. These developments now mean that over-fitting can be avoided when the number of samples is small compared to the number of features. However, it remains unclear whether existing algorithms have the ability to offer good approximations for the task of policy evaluation and improvement. In this paper, we propose a new algorithm for approximating the fixed-point based on the Alternating Direction Method of Multipliers (ADMM). We demonstrate, with experimental results, that the proposed algorithm is more stable for policy iteration compared to prior work. Furthermore, we also derive a theoretical result that states the proposed algorithm obtains a solution which satisfies the optimality conditions for the fixed-point problem.

Structured sparsity approaches have recently received much attention in the statistics, machine learning, and signal processing communities. A common strategy is to exploit or assume prior information about structural dependencies inherent in the data; the solution is encouraged to behave as such by the inclusion of an appropriate regularisation term which enforces structured sparsity constraints over sub-groups of data. An important variant of this idea considers the tree-like dependency structures often apparent in wavelet decompositions. However, both the constituent groups and their associated weights in the regularisation term are typically defined a priori. We here introduce an adaptive wavelet denoising framework whereby a sparsity-inducing regulariser is modified based on information extracted from the signal itself. In particular, we use the same wavelet decomposition to detect the location of salient features in the signal, such as jumps or sharp bumps. Given these locations, the weights in the regulariser associated to the groups of coefficients that cover these time locations are modified in order to favour retention of those coefficients. Denoising experiments show that, not only does the adaptive method preserve the salient features better than the non-adaptive constraints, but it also delivers significantly better shrinkage over the signal as a whole.

The use of sparsity to encourage parsimony in graphical models continues to attract much attention at the interface between multivariate Signal Processing and Statistics. We propose and investigate two approaches for the detection of changepoints in the correlation structure of evolving Gaussian graphical models. Both approaches employ two-stages; first estimating the dynamic graphical structure through regularising the precision matrix, before changepoints are selected via a group fused lasso. Experiments on simulated data illustrate the efficacy of the two approaches. Furthermore, results on real internet traffic flow data containing a Denial Of Service attack demonstrate that the proposed approaches have potential utility in information forensics and security.

Semi-local Hurst estimation is considered for random fields where the regularity varies in a piecewise manner. The recently developed generalised lasso is exploited to propose a spatially regularised Hurst estimator. Dual-tree complex wavelets are used to formulate the usual log-spectrum regression problem and an interlaced penalty matrix is constructed to form a 2-d fused lasso constraint on the double-indexed parameters. We thus extend a regularity-based denoising approach and demonstrate the utility of our method with experiments.

The automatic extraction of elongated curvilinear structures (CLSs) is an important task in various image processing applications, including numerous remote sensing, and biometrical and medical problems. To address this task, we develop a stochastic approach that relies on a fixed-grid, localized Radon transform for line segment extraction and a conditional random field model to incorporate local interactions and refine the extracted CLSs. We propose several different energy data terms, the appropriate choice of which allows us to process images with different noise and geometry properties. The contribution of this paper is the design of a flexible and robust elongated CLS extraction framework that is comparatively fast due to the use of a fixed-grid configuration and fast deterministic Radon-based line detector. We present several different applications of the developed approach, namely: 1) CLS extraction in mammographic images; 2) road networks extraction from optical remotely sensed images; and 3) line extraction from palmprint images. The experimental results demonstrate that the method is fairly robust to CLS curvature and can accurately extract blurred and low-contrast elongated CLS.

An anomaly detection approach is considered for the mine hunting in sonar imagery problem. The authors exploit previous work that used dual-tree wavelets and fractal dimension to adaptively suppress sand ripples and a matched filter as an initial detector. Here, lacunarity inspired features are extracted from the remaining false positives, again using dual-tree wavelets. A one-class support vector machine is then used to learn a decision boundary, based only on these false positives. The approach exploits the large quantities of ‘normal’ natural background data available but avoids the difficult requirement of collecting examples of targets in order to train a classifier.

Polar matching is a recently developed shift and rotation invariant object detection method that is based upon dual-tree complex wavelet transforms or equivalent multiscale directional filterbanks. It can be used to facilitate both keypoint matching, neighborhood search detection, or detection and tracking with particle filters. The theory is extended here to incorporate an allowance for local spatial and dilation perturbations. With experiments, we demonstrate that the robustness of the polar matching method is strengthened at modest computational cost.

The dual-tree wavelet transform is here applied to the problem of fractal dimension estimation. The Hurst parameter of fractional Brownian surfaces is estimated using various wavelet bases. Results are given for global, local, anisotropic, and both local and anisotropic Hurst parameters. It is shown that the directional selectivity of the dual-tree wavelets can be exploited effectively to compute and distinguish Hurst parameters that vary non-trivially with direction and space.

Previous research applying kernel methods such as support vector machines (SVMs) to hyperspectral image classification has achieved performance competitive with the best available algorithms. However, few efforts have been made to extend SVMs to cover the specific requirements of hyperspectral image classification, for example, by building tailor-made kernels. Observation of real-life spectral imagery from the AVIRIS hyperspectral sensor shows that the useful information for classification is not equally distributed across bands, which provides potential to enhance the SVM's performance through exploring different kernel functions. Spectrally weighted kernels are, therefore, proposed, and a set of particular weights is chosen by either optimizing an estimate of generalization error or evaluating each band's utility level. To assess the effectiveness of the proposed method, experiments are carried out on the publicly available 92AV3C dataset collected from the 220-dimensional AVIRIS hyperspectral sensor. Results indicate that the method is generally effective in improving performance: spectral weighting based on learning weights by gradient descent is found to be slightly better than an alternative method based on estimating "relevance" between band information and ground truth.

The purpose of the Applied Multi-dimensional Fusion Project is to investigate the benefits that data fusion and related techniques may bring to future military Intelligence Surveillance Target Acquisition and Reconnaissance systems. In the course of this work, it is intended to show the practical application of some of the best multi-dimensional fusion research in the UK. This paper highlights the work done in the area of multi-spectral synthetic data generation, super-resolution, joint fusion and blind image restoration, multi-resolution target detection and identification and assessment measures for fusion. The paper also delves into the future aspirations of the work to look further at the use of hyper-spectral data and hyper-spectral fusion. The paper presents a wide work base in multi-dimensional fusion that is brought together through the use of common synthetic data, posing real-life problems faced in the theatre of war. Work done to date has produced practical pertinent research products with direct applicability to the problems posed.

Spectral band selection is a fundamental problem in hyperspectral data processing. In this letter, a new band-selection method based on mutual information (MI) is proposed. MI measures the statistical dependence between two random variables and can therefore be used to evaluate the relative utility of each band to classification. A new strategy is described to estimate the MI using a priori knowledge of the scene, reducing reliance on a "ground truth" reference map, by retaining bands with high associated MI values (subject to the so-called "complementary" conditions). Simulations of classification performance on 16 classes of vegetation from the AVIRIS 92AV3C data set show the effectiveness of the method, which outperforms an MI-based method using the associated reference map, an entropy-based method, and a correlation-based method. It is also competitive with the steepest ascent algorithm at much lower computational cost