Periodic Splines and Gaussian Processes for the Resolution of Linear Inverse Problems
Anaïs Badoual, EPFL STI LIB

Meeting • 30 January 2018

Abstract
This presentation deals with the resolution of inverse problems in a periodic setting or, in other terms, the reconstruction of periodic continuous-domain signals from their noisy measurements. We focus on two reconstruction paradigms. In the variational approach, the reconstructed signal is solution of an optimization problem that combines the fidelity to the data and imposes some smoothness conditions via a quadratic regularization associated to a linear operator. In the statistical approach, the signal is modeled as a stationary random process defined from a Gaussian white noise and a whitening operator. One then looks for the optimal estimator in the mean-square sense. For the two approaches, we give a generic form of the reconstructed signals for a broad class of problems. The specificity of this work is to provide a very general analysis and comparison of the two approaches for periodic signals.