Prof. Demetrio Labate University of Huston, USA - 24/05/18
Prof. Demetrio Labate University of Huston, USA - 24/05/18
Seminario del giorno 24 maggio ore 10:
"Sparsity-based computed tomography and region-of-interest tomographic reconstruction".
Abstract: Computed tomography is a non-invasive scanning method that is
widely employed in medical and industrial imaging to reconstruct the
unknown interior structure of an object from a collection of projection
images. The mathematical problem of recovering an unknown density
function from its linear projections is a classical ill-posed problem,
and many methods have been proposed and applied in the literature. This
talk will be divided into two parts.
The first part will discuss classical and more advanced methods of
regularized tomographic reconstruction. In particular, we show how a
wavelet-vaguelette decomposition of the Radon operator can take
advantage of sparse multiscale representations to obtain regularized
reconstruction outperforming more conventional regularization methods.
In the second part of the talk, we consider region-of-interest (ROI)
tomographic reconstruction - a particularly
challenging mathematical and computational problem. Using an appropriate
sparsity prior based on the theory of compressed sensing, we derive
performance guarantees for ROI tomographic reconstruction by
establishing error bounds for stable recovery. We show numerical tests
from experimental data to compare sparsity-based and state-of-the-art
reconstruction methods.
L'incontro sara'organizzato in due parti con breve interruzione nel mezzo.
La prima parte sara'piu' didattica mentre la seconda parte sara' piu'
orientata alla ricerca. Le conoscenze preliminari richieste sono la
trasformata di Fourier.