Professor of Mathematics and Computer Sciences (1981)
B.Sc. (Hon.), mathematics, University of Windsor, 1976; S.M., mathematics, University of Chicago, 1978; Ph.D., mathematics, University of Chicago, 1981.
Professor Lucier's recent research covers two areas: the application of moving-grid and free-knot-spline approximation techniques to the theoretical study and numerical approximation of time-dependent partial differential equations, and the application of wavelet techniques to data compression (particularly image and surface compression), image processing (particularly noise reduction in images), and smoothing spline models in statistics. This work, conducted for the most part with Ronald A. DeVore of the University of South Carolina, is based on recent theoretical results on nonlinear approximation of functions (surfaces, images, solutions of differential equations) with minimal smoothness. Such a theory is necessary for the study of images (which generally exhibit discontinuities in intensity), solutions of the equations of inviscid gas dynamics (for which the density may be discontinuous in supersonic flows, for example), and surfaces (which may have cusps (point singularities) or creases, along which the gradient is discontinuous). This work has introduced new compression techniques and led to new ways of understanding previous techniques, such as the effects of quantizing image transform coefficients.
Projects: Regularity and Approximation for Hyperbolic Conservation Laws in Several Space Dimensions