Frank Geshwind

Discriminant feature extraction using empirical probability density estimation and a local basis library

The authors previously developed the so-called local discriminant basis (LDB) method for signal and image classi3cation problems. The original LDB method relies on di4erences in the time–frequency energy distribution of each class: it selects the subspaces where these energy distributions are well separated by some measure such as the Kullback–Leibler divergence. Through our experience and experiments on various datasets, however, we realized that the time–frequency energy distribution is not always the best quantity to analyze for classi3cation. In this paper, we propose to use the discrimination of coordinates based, instead, on empirical probability densities. That is, we estimate the probability density of each class in each coordinate in the wavelet packet=local trigonometric bases after expanding signals into such bases. We then evaluate a power of discrimination of each subspace by selecting the m most discriminant coordinates in terms of the “distance” among the corresponding densities (e.g., by the Kullback–Leibler divergence among the densities). This information is then used for selecting a basis for classi3cation. We will demonstrate the capability of this algorithm using both synthetic and real datasets. ? 2002 Pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserved.

Application of spatial light modulators for new modalities in spectrometry and imaging

We have constructed an adaptive digitally tuned light source in the form of a de-dispersive imaging spectrograph in both the visible and near infrared spectral regions capable of illuminating a sample with appropriate energy weighted spectral bands or spatio-spectral bands that relate only to the constituents of interest to the investigator. The energy from each of the spectral resolution elements can be digitally modulated to provide a tuned weighted spectral output. A tuned light source based on this technology was adapted for use in a conventional imaging microscope system to enable direct measure of spatio-spectral features of interest. Some imagery resulting from preliminary tests on colon tissue biopsies are presented.

Hyperspectral microscopic analysis of normal, benign and carcinoma microarray tissue sections

We apply a unique micro-optoelectromechanical tuned light source and new algorithms to the hyper-spectral microscopic analysis of human colon biopsies. The tuned light prototype (Plain Sight Systems Inc.) transmits any combination of light frequencies, range 440nm 700nm, trans-illuminating H and E stained tissue sections of normal (N), benign adenoma (B) and malignant carcinoma (M) colon biopsies, through a Nikon Biophot microscope. Hyper-spectral photomicrographs, randomly collected 400X magnication, are obtained with a CCD camera (Sensovation) from 59 different patient biopsies (20 N, 19 B, 20 M) mounted as a microarray on a single glass slide. The spectra of each pixel are normalized and analyzed to discriminate among tissue features: gland nuclei, gland cytoplasm and lamina propria/lumens. Spectral features permit the automatic extraction of 3298 nuclei with classification as N, B or M. When nuclei are extracted from each of the 59 biopsies the average classification among N, B and M nuclei is 97.1%; classification of the biopsies, based on the average nuclei classification, is 100%. However, when the nuclei are extracted from a subset of biopsies, and the prediction is made on nuclei in the remaining biopsies, there is a marked decrement in performance to 60% across the 3 classes. Similarly the biopsy classification drops to 54%. In spite of these classification differences, which we believe are due to instrument and biopsy normalization issues, hyper-spectral analysis has the potential to achieve diagnostic efficiency needed for objective microscopic diagnosis.

Pseudodifferential operators onSU(2)

We construct an algebra of left-invariant pseudodifferential operators on SU(2). We require only that the symbols be homogeneous and C2. For Fourier-bandlimited symbols, we derive the expected formulae for composition and commutators and construct an orthonormal basis of common approximate eigenvectors that could be used to study spectral theory. Some remarks on applications to matrices of operators are made.

Approximate frames and the narrowband multitarget radar problem

Certain applications in narrowband radar require either that the windowed Fourier transform or the Weyl-Heisenberg wavelet expansion of a signal be computed. Under narrowband assumptions, and in general for real applications, it is necessary for the window signal to have finite first and second time and frequency moments, but Balian’s theorem shows that, in this case, the windowed basis is never a frame. This paper describes an approximation method which will allow stable calculation in this situation, even though the signals that must be used never give rise to frames. Using density properties of certain sets in an appropriate function space, it is seen that the set of frames and the set of certain “nice” signals can each approximate elements of each other, to within an arbitrary degree of accuracy. This yields a method for studying radar problems with a given signal, as well as a method for constructing signals which ought to be good for radar applications.