Christopher V. Alvino

Geometric source separation: merging convolutive source separation with geometric beamforming

Convolutive blind source separation and adaptive beamforming have a similar goal-extracting a source of interest (or multiple sources) while reducing undesired interferences. A benefit of source separation is that it overcomes the conventional cross-talk or leakage problem of adaptive beamforming. Beamforming on the other hand exploits geometric information which is often readily available but not utilized in blind algorithms. We propose to join these benefits by combining cross-power minimization of second-order source separation with geometric linear constraints used in adaptive beamforming. We find that the geometric constraints resolve some of the ambiguities inherent in the independence criterion such as frequency permutations and degrees of freedom provided by additional sensors. We demonstrate the new method in performance comparisons for actual room recordings of two and three simultaneous acoustic sources.

Single-trial detection in EEG and MEG: Keeping it linear

Conventional electroencephalography (EEG) and magnetoencephalography (MEG) analysis often rely on averaging over multiple trials to extract statistically relevant di7erences between two or more experimental conditions. We demonstrate that by linearly integrating information over multiple spatially distributed sensors within a prede9ned time window, one can discriminate conditions on a trial-by-trial basis with high accuracy. We restrict ourselves to a linear integration as it allows the computation of a spatial distribution of the discriminating source activity. In the present set of experiments the resulting source activity distributions correspond to functional neuroanatomy consistent with the task (e.g. contralateral sensory-motor cortex and anterior cingulate). c � 2003 Elsevier Science B.V. All rights reserved.

Tomographic reconstruction of piecewise smooth images

In computed tomography, direct inversion of the Radon transform requires more projections than are practical due to constraints in scan time and image accessibility. Therefore, it is necessary to consider the estimation of reconstructed images when the problem is under-constrained, i.e., when a unique solution does not exist. To resolve ambiguities among solutions, it is necessary to place additional constraints on the reconstructed image. In this paper, we present a surface evolution technique to model the reconstructed image as piecewise smooth. We model the reconstructed image as two regions that are each smoothly varying in intensity and are separated by a smooth surface. We define a cost functional to penalize deviation from piecewise smoothness while ensuring that the projections of the estimated image match the measured projections. From this functional, we derive an evolution for the modeled image intensity and an evolution for the surface, thereby defining a variational tomographic estimation technique. We show example reconstructions to highlight the performance of the proposed method on real medical images.

Fast Mumford-Shah segmentation using image scale space bases

Image segmentation using the piecewise smooth variational model proposed by Mumford and Shah is both robust and computationally expensive. Fortunately, both the intermediate segmentations computed in the process of the evolution, and the final segmentation itself have a common structure. They typically resemble a linear combination of blurred versions of the original image. In this paper, we present methods for fast approximations to Mumford-Shah segmentation using reduced image bases. We show that the majority of the robustness of Mumford-Shah segmentation can be obtained without allowing each pixel to vary independently in the implementation. We illustrate segmentations of real images that show how the proposed segmentation method is both computationally inexpensive, and has comparable performance to Mumford-Shah segmentations where each pixel is allowed to vary freely.

Multigrid computation of rotationally invariant non-linear optical flow

In supplement to an earlier paper, we present an altered cost functional for the computation of an edge-preserving optical flow that is invariant to rotation. In addition, we explain how the solutions to the resulting non-linear partial differential equations may be computed more efficiently with non-linear multigrid techniques. We prove the rotational invariance of this functional and report computation times on a real image sequence.

A scale space for contour registration using minimal surfaces

Previously, we presented a method for contour registration using minimal surfaces. This method involves embedding each of two unregistered two-dimensional contours into two parallel planes separated in three-dimensional space. The minimal surface is then computed between the two contours via mean curvature flow. We then evolve the rigid registration of one of the two contours which in turn changes the minimal surface. Mean curvature flow of the surface and evolution of the curve registration both support a consistent energy functional, i.e., area of the connecting surface. We review the implementation details and show an example registration. In this paper we concentrate on developing this method as a registration scale space. The separation of the two contour planes serves as a scale space parameter, larger separations producing coarser registrations. At the finest scale, which occurs as the separation distance approaches zero, this registration method is identical to minimizing the set-symmetric difference between the interiors of the contours. Thus, this method can be viewed as a geometric generalization of set-symmetric difference registration. We explain the scale space properties of this registration method theoretically and experimentally. Through examples we show how at increasingly coarser scales, our method overcomes increasingly coarser local minima apparent in set-symmetric difference registration. In addition, we present sufficient conditions for existence of the minimal surface connecting two contours. This condition yields an upper bound for the separation distance between two contours and gives an estimate for the coarsest registration scale.