Multiscale object features from clustered complex wavelet coefficients

This paper introduces a method by which intuitive feature entities can be created from ILP (InterLevel Product) coefficients. The ILP transform is a pyramid of decimated complex-valued coefficients at multiple scales, derived from dual-tree complex wavelets, whose phases indicate the presence of different feature types (edges and ridges). We use an Expectation-Maximization algorithm to cluster large ILP coefficients that are spatially adjacent and similar in phase. We then demonstrate the relationship that these clusters possess with respect to observable image content, and conclude with a look at potential applications of these clusters, such as rotation- and scale-invariant object recognition. © 2005 IEEE.

Statistical image modelling using interscale phase relationships of complex wavelet coefficients

A novel method for modelling the statistics of 2D photographic images useful in image restoration is defined. The new method is based on the Dual Tree Complex Wavelet Transform (DT-CWT) but a phase rotation is applied to the coefficients to create complex coefficients whose phase is shift-invariant at multiscale edge and ridge features. This is in addition to the magnitude shift invariance achieved by the DT-CWT. The increased correlation between coefficients adjacent in space and scale provides an improved mechanism for signal estimation. © 2006 IEEE.

DT-MRI data visualisation using the dual tree Complex Wavelet transform

In this paper a novel visualisation method for diffusion tensor MRI datasets is introduced. This is based on the use of Complex Wavelets in order to produce "stripy" textures which depict the anisotropic component of the diffusion tensors. Grey-scale pixel intensity is used to show the isotropic component. This paper also discusses enhancements of the technique for 3D visualisation. © 2004 IEEE.

Convex approaches to model wavelet sparsity patterns

Statistical dependencies among wavelet coefficients are commonly represented by graphical models such as hidden Markov trees (HMTs). However, in linear inverse problems such as deconvolution, tomography, and compressed sensing, the presence of a sensing or observation matrix produces a linear mixing of the simple Markovian dependency structure. This leads to reconstruction problems that are non-convex optimizations. Past work has dealt with this issue by resorting to greedy or suboptimal iterative reconstruction methods. In this paper, we propose new modeling approaches based on group-sparsity penalties that leads to convex optimizations that can be solved exactly and efficiently. We show that the methods we develop perform significantly better in de-convolution and compressed sensing applications, while being as computationally efficient as standard coefficient-wise approaches such as lasso. © 2011 IEEE.

Fractal dimension, wavelet shrinkage and anomaly detection for mine hunting

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. © 2012 The Institution of Engineering and Technology.

Atmospheric turbulence mitigation using complex wavelet-based fusion

Restoring a scene distorted by atmospheric turbulence is a challenging problem in video surveillance. The effect, caused by random, spatially varying, perturbations, makes a model-based solution difficult and in most cases, impractical. In this paper, we propose a novel method for mitigating the effects of atmospheric distortion on observed images, particularly airborne turbulence which can severely degrade a region of interest (ROI). In order to extract accurate detail about objects behind the distorting layer, a simple and efficient frame selection method is proposed to select informative ROIs only from good-quality frames. The ROIs in each frame are then registered to further reduce offsets and distortions. We solve the space-varying distortion problem using region-level fusion based on the dual tree complex wavelet transform. Finally, contrast enhancement is applied. We further propose a learning-based metric specifically for image quality assessment in the presence of atmospheric distortion. This is capable of estimating quality in both full-and no-reference scenarios. The proposed method is shown to significantly outperform existing methods, providing enhanced situational awareness in a range of surveillance scenarios. © 1992-2012 IEEE.