J. D. B. Nelson

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—Sand ripples present a difficult challenge to current mine hunting approaches. We propose a robust and adaptive method that suppresses sand ripples prior to the detection stage. The method exploits a fractal model of the seabed and the connection between: dual-tree wavelets and local, directional fractal dimension; interscale energy ratios, scale invariant(More)
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(More)
—The detection and tracking of targets in aerial imagery of cluttered urban environments is addressed. Polar matching, using dual-tree complex wavelet transforms, is used as a shift and rotation invariant detector. A particle filter is employed to add robustness, especially in the event of target occlusion. We show that, together, these methods can robustly(More)
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(More)
Semi-local Hurst estimation is considered by incorporating a Markov random field model to constrain a wavelet-based pointwise Hurst estimator. This results in an estimator which is able to exploit the spatial regularities of a piecewise parametric varying Hurst parameter. The pointwise estimates are jointly inferred along with the parametric form of the(More)
A generalised Lasso iteratively reweighted scheme is here introduced to perform spatially regularised Hurst estimation on semi-local, weakly self-similar processes. This is extended further to the robust, heavy-tailed case whereupon the generalised M-Lasso is proposed. The design successfully incorporates both a spatial derivative in the generalised Lasso(More)
A recent dual-tree wavelet shrinkage method to suppress sand ripples in sonar imagery is extended with a Markov random field framework. Markov chain Monte Carlo sampling is used to estimate the posterior marginal ripple state in the wavelet domain. Ripple suppression is realised by multiplying the dual-tree wavelet coefficients by the conditional(More)
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(More)