Mathematics Colloquium: Images, PDEs and Wavelets
4:10 pm. Neill Hall 5W
Abstract: Wavelets and PDEs have had profound impacts on imaging sciences. Their successes rely on their remarkable mathematical properties, many of which are complementary to each other. In this talk, I will present an overview of our work along the direction of merging them to further improve the performance, as well as to model new applications in image processing. A main goal is to handle sharp discontinuities stably and robustly. The main approach combines regularity control using PDEs while manipulating coefficients in wavelet space. Applications include image compression, denoising, and wavelet inpainting. Connections with compressed sensing will be made.