Wayne M. Lawton (Dept of Mathematics, National University of Singapore) Title: Spatially Adaptive Learning Theory Abstract: We consider the problem of 'reconstructing' an image from samples where (i) it is reasonable to assume that the image was smooth in some heuristic sense, (ii) the sample locations are not uniformly spaced, and (iii) the sample values may have some error. One approach expresses the reconstructed image as a linear combination of kernel functions centered at the sample locations whose coefficients are chosen so that the reconstructed image interpolates the sample values. Another approach computes the reconstructed image so as to minimize a norm. We consider the relationship between these approaches, stipulate criteria for choosing the kernel functions and norms, and the constructiuon of kernels and norms from wavelets and Greens functions. *********************************************************************************** Short CV of Wayne M. Lawton Present Appointment: Associate Professor Contact Information: Department of Mathematics Faculty of Science National University of Singapore 2 Science Drive 2 Singapore 117543 Tel: (65) 874-2749; fax: (65) 779-5452; email: matwml@nus.edu.sg Research Areas: Classical Analysis and Mathematical Physics Teaching Areas: Approximation Theory, Functional Analysis, Matrix Computation, Classical Mechanics, Mathematical Modelling, Filterbanks and Wavelets, Partial Differential Equations, Stochastic Processes Academic/Professional Qualifications: * BA, PhD (Topological Dynamics), Mathematics (1972), Wesleyan University, Connecticut, USA Awards/Honours (Post-PhD): * Bausch and Lomb Science Award (1968) * Phi Beta Kappa, Sigma Xi, Rice Math Prize (1972) * Marquis Who¡¯s Who in the World and in Science and Engineering (1998) * National Science Award, NSTB, Republic of Singapore (1998) Career History: * Associate Professor of Mathematics, National University of Singapore (January 1999-Present) * Previous Positions: Rice University, University of Houston, Institute for Advanced Study (Princeton), University of Petroleum and Minerals (Saudi Arabia), Chiang Mai University (Thailand), UCLA, USC, Northeast and Boston Universities; MRJ, ERIM, JPL, TRW, Aware Inc. Consultancies: The Analytic Sciences Corporation, NASA, Lockheed, Devaney Associates, a prominent intellectual property law firm in Washington D.C. and other firms (who requested to be anonymous), was also previously employed for 4 years by the Institute of Systems Science in Singapore Administrative Leadership: Deputy Director of the Centre for Industrial Mathematics Chair of Committee on the Special Program in Science Professional/Consulting Activities: * Gave invited talks at numerous international conferences and collaborate with researchers in USA, Europe, China, Japan, Korea, Thailand, Australia. * Ran my own consulting company (1991-1993) in Boston Major Publications (Maximum of 3): * (2000), Transactions of the American Mathematical Society, 352(6), 2913-2936, Infinite convolution products and refinable distributions on Lie groups. * (2001) (with L. Noakes), Computing the inertia operator of a rigid body, Journal of Mathematical Physics, volume 42, number 4, pages 1-11, April 2001. * (2002)The inverse problem for Euler's equation on two and three dimensional Lie groups", ScienceAsia, volume 28, number 1, April 2002.