EU Regional School - DeVore Seminar

Prof. DeVore - Bringing Signals and Images into the Digital World

Department of Mathematics
Texas A&M University


The digital world is preferred for signal and image processing since one can take advantage of the fact that only a finite set of possibilities exist when doing arithmetic computation. On the other hand, most signals are inherently analog. This make the operations of Analog to Digital conversion (A/D) and the reverse Digital to Analog conversion (D/A) cornerstones of signal processing.  
The first lecture will develop the story of how one should perform this conversion from the viewpoints of both mathematicians and engineers. The mathematical solution (Pulse Code Modulation) does not match the preferred engineering solution (Sigma-Delta modulation). We shall try to explain some possible mathematical reasons why Engineers often choose Sigma-Delta Modulation over more obvious and seemingly better choices. 
The second lecture will discuss the representations of images with the goal of deciding how to best achieve compression and denoising. Such image processing tasks require model classes for images in order to build a coherent theory. We shall explain how this leads to the subjects of multiscale decompositions, sparsity, and tree representations that are dominant in image processing and related areas such as modeling terrain surfaces.