Ron Levie (Tel-Aviv University)
It is well known that certain classes of signals can be effectively represented using a wavelet basis or a wavelet frame, keeping only a sparse number of coefficients. For example, Shearlet (discrete) frames are optimally sparse for cartoon like images. In this talk I will extend this approach to continuous wavelet systems, which comprise a continuum of "dictionary" elements. To overcome some of the challenges in the continuous realm, I will present an extension of the standard continuous wavelet theory, called the wavelet-Plancherel theory. Basing our sparse decomposition algorithm on the new theory, we can outperform naive sparse decomposition algorithms.