The main goal of this project is to develop an analytical, multidisciplinary approach to research and education in Image Processing, integrating important aspects of engineering problems that are often treated separately. In particular, this study incorporates realistic statistical models for image data and physical sensors, and seeks solutions to estimation and compression problems based upon fundamental statistical principles. The educational component of this project aims at better preparing students for their engineering careers by developing their multidisciplinary and analytical skills, and exposing them to multiple facets of complex engineering problems. This theme is present at all levels of this project: Firstly, motivated undergraduate students are encouraged to participate in the research. Secondly, an undergraduate Image and Video Processing course and laboratory exercises allow the students to learn, visualize and assimilate fundamental concepts. Thirdly, an advanced graduate Statistical Image Processing course is being developed with the objective of integrating, applying and solidifying concepts taught in Information Theory, Estimation Theory, and Statistical Optics. Fourthly, an interactive, virtual Image Processing lab is being developed as part of two Distance Learning projects. The research component of this project addresses key problems in image restoration and compression and quantifies the benefits that may result from the use of more accurate and sophisticated models. The methodology developed is also applicable to ill-posed statistical inverse problems such as Synthetic Aperture Radar imaging, astronomical imaging, and tomography. Complexity regularization theory plays a central role in this research. Complexity-regularized estimators are inherently in compressed form, and fundamental relationships between estimation performance and rate-distortion theory are explored in that context. Additionally, novel techniques for optimizing for optimizing the operational rate-distortion performance of several image coding systems are being developed.
