"Sparse continuous wavelet transforms via a wavelet-Plancherel theory"
Levie, RonIt 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. In this talk we extend sparse decomposition to the continuous realm, and introduce a sparse decomposition approach for continuous wavelet systems. To overcome the challenges in the continuous realm, we present an extension of the standard continuous wavelet theory, called the wavelet-Plancherel theory. Basing our sparse decomposition algorithm on the new theory, we improve the computational complexity of naive continuous sparse decomposition algorithms. Moreover, the computational complexity of the new method is equal to that of a discrete method, while squaring the sampling resolution in phase space.