Fast minimization of structural risk by nearest neighbor rule.

In this paper, we present a novel nearest neighbor rule-based implementation of the structural risk minimization principle to address a generic classification problem. We propose a fast reference set thinning algorithm on the training data set similar to a support vector machine (SVM) approach. We then show that the nearest neighbor rule based on the reduced set implements the structural risk minimization principle, in a manner which does not involve selection of a convenient feature space. Simulation results on real data indicate that this method significantly reduces the computational cost of the conventional SVMs, and achieves a nearly comparable test error performance.

Image segmentation and edge enhancement with stabilized inverse diffusion equations.

We introduce a family of first-order multidimensional ordinary differential equations (ODEs) with discontinuous right-hand sides and demonstrate their applicability in image processing. An equation belonging to this family is an inverse diffusion everywhere except at local extrema, where some stabilization is introduced. For this reason, we call these equations "stabilized inverse diffusion equations" (SIDEs). Existence and uniqueness of solutions, as well as stability, are proven for SIDEs. A SIDE in one spatial dimension may be interpreted as a limiting case of a semi-discretized Perona-Malik equation. In an experiment, SIDE's are shown to suppress noise while sharpening edges present in the input signal. Their application to image segmentation is also demonstrated.

Multiscale segmentation and anomaly enhancement of SAR imagery.

We present efficient multiscale approaches to the segmentation of natural clutter, specifically grass and forest, and to the enhancement of anomalies in synthetic aperture radar (SAR) imagery. The methods we propose exploit the coherent nature of SAR sensors. In particular, they take advantage of the characteristic statistical differences in imagery of different terrain types, as a function of scale, due to radar speckle. We employ a class of multiscale stochastic processes that provide a powerful framework for describing random processes and fields that evolve in scale. We build models representative of each category of terrain of interest (i.e., grass and forest) and employ them in directing decisions on pixel classification, segmentation, and anomalous behaviour. The scale-autoregressive nature of our models allows extremely efficient calculation of likelihoods for different terrain classifications over windows of SAR imagery. We subsequently use these likelihoods as the basis for both image pixel classification and grass-forest boundary estimation. In addition, anomaly enhancement is possible with minimal additional computation. Specifically, the residuals produced by our models in predicting SAR imagery from coarser scale images are theoretically uncorrelated. As a result, potentially anomalous pixels and regions are enhanced and pinpointed by noting regions whose residuals display a high level of correlation throughout scale. We evaluate the performance of our techniques through testing on 0.3-m resolution SAR data gathered with Lincoln Laboratory's millimeter-wave SAR.

Temporal and spatial analysis of potential maps via multiresolution decompositions.

Cardiac potentials recorded on the epicardium or the body surface by an array of electrodes are usually analyzed either as spatial distributions or temporal waveforms. Thus, the analysis often involves temporal descriptors (eg. max dV/dt) or spatial descriptors (eg. location of local extrema) only. The best known transform technique that has been applied to these data that combines both spatial and temporal characteristics is the Karhunen-Loeve transform, a global transform applied to temporal and/or spatial bases obtained by statistical analysis of a database. As an alternative, multiresolution decompositions and related wavelet-type transforms have recently seen great development in signal processing and related fields. They offer flexibility, employing transformations onto local (rather than global) and fixed (rather than data-dependent) databases, and allow transformation of distributions, waveforms, or both, as desired. The utility of this method as applied to temporal and spatial segmentation and analysis of map data from both epicardial plaques and body surface potentials recorded during percutaneous transluminal coronary angioplasty is illustrated.

Analysis of PTCA-induced ischemia using an ECG inverse solution or the wavelet transform.

In patients without significant collaterals, percutaneous transluminal coronary angioplasty (PTCA) produces acute transient ischemia that is detectable in both standard electrocardiograms (ECG) and body surface potential maps (BSPMs). Control recordings made before or between inflations provide personalized baselines, which isolate the effects of ischemia from interpatient differences, such as torso shape and electrode location. In this study, two methods of evaluating PTCA-induced ischemia from BSPM recordings are presented. In the first method, an ECG inverse solution that estimates epicardial potentials from body surface signals using a realistic model of torso geometry is applied. The strength of this method lies in its potential ability to localize areas of cardiac ischemia on the epicardial surface. In the second approach, wavelet transforms were used to perform a multiresolution decomposition of the BSPM data into different frequency bands. The basis functions of the wavelet transform are time-limited and narrow band and hence can be expected to be sensitive to features of the BSPM that originate in discrete electrophysiologic events, such as intrusion of the activation front onto regions of ischemia or arrhythmias due to local conduction abnormalities. The method also offers a means of temporal and frequency localization of cardiac events related to the initiation of injury currents and abnormal conduction due to PTCA-induced ischemia. The inverse solution and the wavelet transform each offer new views of the spatial and temporal courses of acute ischemia potentially leading to new diagnostic insights in ECG patient examination.