Ozan Öktem, KTH SCI

In many applications the measured data has significant amount of noise. Furthermore, data may be incomplete in the sense that it is non-uniformly sampled and(or) significant amount of it is missing (incomplete data). Signal processing under these conditions is very difficult and a variety of computational approaches have been developed for addressing such challenges. Many of these approaches were problem specific. However, the most successful ones did share a common feature in that they properly accounted for patterns in the signal/data. This observation was the starting point for the development of sparse signal processing, a general mathematical framework for signal processing developed specifically to deal with sparse signals. The underlying basic idea is that almost all real-world signals have an underlying pattern, hence viewed mathematically, such signals also have low information content since these patterns can be utilised for providing a good description of the signal. Sparse signal processing is a general mathematical framework for modelling and systematically extracting such patterns in the signal from direct or indirect observations (data). It turns out that algorithms developed from the general theory of sparse signal processing compete favourably with application specific state-of-the-art approaches. This is especially the case for situations with incomplete data and(or) highly noisy data, cases that previously were considered impossible to handle. The talk will illustrate these claims in a manner accessible for the non-expert.