Znanstveni kolokviji

Sparse approximation techniques have been at the core of a rapidly evolving and very active area of research since the 1990s. Their most visible technological success has certainly been in the compression of high-dimensional data with wavelets. However, approximating a signal or an image with a sparse liner expansion from a possibly overcomplete dicctionary of basis functions (called atoms) has turned out to be an extremely useful tool to solve many other signal processing problems. In this talk, I will discuss some of the mathematical and computational aspects of sparse representations using redundant dictionaries in a Hilbert space. Our main focus will be on sparse representations using 'coherent' dictionaries in a finite dimensional space, but we will also mention some very recent results on infinite dimensional time-frequency dictionaries that have clusters of coherent atoms.