In step with each technological breakthrough, increasingly more of what we learn about the world is measured indirectly. Extending and complementing our sensory faculties, we rely on technology to probe across long distances and through natural barriers. Astronomy, nondestructive testing, medical imaging, and geophysical prospecting are all important examples of our ability to make indirect measurements of a physical effect and from these learn about the causes of such effects. At the heart of this ability are inverse methods: practical computational techniques for processing the measured data and distilling the information of interest from the data. These techniques bring together tools from multidimensional signal processing, statistics, and applied mathematics.
The purpose of this CAREER grant proposal is the development of a long term research and educational program in multidimensional signal processing that will integrate engineering, statistical, and numerical techniques for the solution of inverse problems in imaging. The educational component of the proposed program will design, from the ground level, a comprehensive graduate and undergraduate curriculum in statistical signal and image processing at the newly established department of Electrical Engineering at the University of California, Santa Cruz. In addition, an introductory undergraduate seminar course, and an in-depth graduate course on the subject of in- verse problems in imaging will be developed. The research component of the proposed program will address problems in image reconstruction from indirectly measured information that may be in- complete and noisy. These data can convey information that, depending upon the application, may be geometric in nature (2-D silhouettes of a 3-D object), tomographic (projections of a function), local (blurred and downsampled images of a detailed scene), or global (moments of an object.) Our program of research will entail the development of statistical and numerical methods for solving problems in each of the said categories.
