Variational Justification of Cycle Spinning for Inverse Problems
Ulugbek Kamilov, EPFL STI LIB

Seminar • 10 March 2014 • Bm 4.233

Abstract
Estimating a signal from limited and noise-corrupted linear observations is a fundamental problem in signal processing. Wavelet-based methods seek for a signal that admits a sparse representation in the wavelet domain. Cycle spinning is a technique that is commonly used to dramatically improve the performance of standard wavelet-based methods. The algorithm typically “cycle spins” by repeatedly translating and denonising the current estimate via basic wavelet-denoising and then translating back; at each iteration. To date, no theoretical convergence results are known for cycle spinning. Here, we prove that the algorithm is guaranteed to convergence to the minimum of some global cost-function incorporating all wavelet-shifts. The proof relies on the stochastic optimization theory.