ABSTRACT

The multiscale decomposition of images developed by Tadmor, Nezzar and Vese in 2004 has been extended to other imaging applications and to inverse problems, even in the nonlinear case, by Modin, Nachman and myself. About inverse problems, the multiscale procedure always provides a minimising sequence with respect to the error on the measurements, but convergence to a solution of the inverse problem is guaranteed only for a so-called tighter version of the multiscale procedure. It was an open question whether the original multiscale decomposition is enough for such a convergence to hold.

In this talk we consider linear inverse problems and provide both positive and negative answers to this question, thus showing optimality properties of these multiscale procedures.

This is a joint work with Simone Rebegoldi (Università di Modena e Reggio Emilia).