A variational approach to the inversion of truncated Fourier operators

20 pagesInternational audienceTruncated Fourier operators play an important role in many inverse problems of signal and image science. A variational approach to the regularization of their pseudo-inverses is considered. A particular regularization parameter, which can be interpreted in terms of resolution level, appears to play the essential role. This paper presents results on the behavior of the regularized solution as this parameter tends to zero. Notably, reasonably mild conditions are shown to ensure strong convergence of the regularized solution to the pseudo-inverse of the data