Estimating proportions of objects from multispectral scanner data

Progress is reported in developing and testing methods of estimating, from multispectral scanner data, proportions of target classes in a scene when there are a significiant number of boundary pixels. Procedures were developed to exploit: (1) prior information concerning the number of object classes normally occurring in a pixel, and (2) spectral information extracted from signals of adjoining pixels. Two algorithms, LIMMIX and nine-point mixtures, are described along with supporting processing techniques. An important by-product of the procedures, in contrast to the previous method, is that they are often appropriate when the number of spectral bands is small. Preliminary tests on LANDSAT data sets, where target classes were (1) lakes and ponds, and (2) agricultural crops were encouraging

Scientific Endeavors of A.M. Mathai: An Appraisal on the Occasion of his Eightieth Birthday, April 2015

A.M. Mathai is Emeritus Professor of Mathematics and Statistics at McGill University, Canada, and Director of the Centre for Mathematical and Statistical Sciences, India. He has published over 300 research papers and more than 25 books on topics in mathematics, statistics, physics, astrophysics, chemistry, and biology. He is a Fellow of the Institute of Mathematical Statistics, National Academy of Sciences of India, President of the Mathematical Society of India, and a Member of the International Statistical Institute. He is the founder of the Canadian Journal of Statistics and the Statistical Society of Canada. He is instrumental in the implementation of the United Nations Basic Space Science Initiative. The paper is an attempt to capture the broad spectrum of scientific endeavors of Professor A.M. Mathai at the occasion of his anniversary.Comment: 21 pages, LaTe

Sparse and Non-Negative BSS for Noisy Data

Non-negative blind source separation (BSS) has raised interest in various fields of research, as testified by the wide literature on the topic of non-negative matrix factorization (NMF). In this context, it is fundamental that the sources to be estimated present some diversity in order to be efficiently retrieved. Sparsity is known to enhance such contrast between the sources while producing very robust approaches, especially to noise. In this paper we introduce a new algorithm in order to tackle the blind separation of non-negative sparse sources from noisy measurements. We first show that sparsity and non-negativity constraints have to be carefully applied on the sought-after solution. In fact, improperly constrained solutions are unlikely to be stable and are therefore sub-optimal. The proposed algorithm, named nGMCA (non-negative Generalized Morphological Component Analysis), makes use of proximal calculus techniques to provide properly constrained solutions. The performance of nGMCA compared to other state-of-the-art algorithms is demonstrated by numerical experiments encompassing a wide variety of settings, with negligible parameter tuning. In particular, nGMCA is shown to provide robustness to noise and performs well on synthetic mixtures of real NMR spectra.Comment: 13 pages, 18 figures, to be published in IEEE Transactions on Signal Processin

Shapes of leading tunnelling trajectories for single-electron molecular ionization

Based on the geometrical approach to tunnelling by P.D. Hislop and I.M. Sigal [Memoir. AMS 78, No. 399 (1989)], we introduce the concept of a leading tunnelling trajectory. It is then proven that leading tunnelling trajectories for single-active-electron models of molecular tunnelling ionization (i.e., theories where a molecular potential is modelled by a single-electron multi-centre potential) are linear in the case of short range interactions and "almost" linear in the case of long range interactions. The results are presented on both the formal and physically intuitive levels. Physical implications of the obtained results are discussed.Comment: 14 pages, 5 figure

CFD applications in chemical propulsion engines

The present research is aimed at developing analytical procedures for predicting the performance and stability characteristics of chemical propulsion engines. Specific emphasis is being placed on understanding the physical and chemical processes in the small engines that are used for applications such as spacecraft attitude control and drag make-up. The small thrust sizes of these engines lead to low nozzle Reynolds numbers with thick boundary layers which may even meet at the nozzle centerline. For this reason, the classical high Reynolds number procedures that are commonly used in the industry are inaccurate and of questionable utility for design. A complete analysis capability for the combined viscous and inviscid regions as well as for the subsonic, transonic, and supersonic portions of the flowfield is necessary to estimate performance levels and to enable tradeoff studies during design procedures