Abstract:

In signal/image and data processing in general, we often use 
transforms in order to simplify operations or to enable better 
treatment to the given data. A recent trend in these fields is the 
use of overcomplete linear transforms that lead to a sparse 
description of signals. This new breed of methods is more difficult 
to use, often requiring more computations. Still, they are much more 
effective in applications such as signal compression and inverse 
problems. In fact, much of the success attributed to the wavelet 
transform in recent years, is directly related to the 
above-mentioned trend. In this talk I will present a survey of this 
recent path of research, and its main results. I will discuss both 
the theoretic and the applicative sides to this field. No previous 
knowledge is assumed (... just common sense, and little bit of 
linear algebra).