Hybrid spline dictionaries for continuous-domain inverse problems
Thomas Debarre, EPFL STI LIB

Meeting • 24 April 2018

Abstract
We study 1D continuous-domain inverse problems with multiple gTV (generalized Total-Variation) regularization (i.e. several different regularization operators). This work is based on a continuous-representer theorem, which states that such inverse problems have hybrid spline solutions. The total sparsity of these hybrid splines is bounded by the number of measurement. We show that such continuous-domain problems can be discretized in an exact way by using a union of B-spline dictionaries matched to the regularization operators. We then propose a multiresolution algorithm which selects an appropriate grid size depending on the problem at hand. Finally, we demonstrate the computational feasibility of our algorithm for multiple order derivative regularization operators.