This talk will focus on the robust prediction/estimation of nonstationary signals using adaptive, sparse statistical models. With the aid of nonlinear approximation principles, I will show how some simple signal processing techniques can be generalized to yield significantly more powerful results. I will briefly discuss the mathematical nature of the constructed estimators and the class of signals over which these estimators are expected to perform well in a mean squared error sense.

The estimation framework I will develop is general and can readily be applied to many different types of nonstationary signals, beyond images and video. However, I will concentrate on images, and estimate missing data over locally uniform (smooth, high frequency, texture, etc.) regions separated by edges or edge-like singularities.

I will include an extensive number of example images and video that depict processing results and that show the discussed techniques in action. My examples will include prediction applications (on well known images, and on damaged images of planets sent by space probes) as well as inpainting applications.

The talk will begin with background information and I will also discuss related information theoretic aspects of compression, sparse decompositions, and nonlinear approximation with some further examples.