Seminario de análisis

Viernes, 28 de marzo de 2025,
10:00 - 11:00, Aula 520, departamento de Matemáticas
Matteo Santacesaria

MALGA - Università di Genova

Compressed sensing for the sparse Radon
transform

Resumen:
Compressed sensing allows for the recovery of sparse signals from few measurements,
whose number is proportional, up to logarithmic factors, to the sparsity of the unknown
signal. The classical theory mostly considers either random linear measurements or
subsampled isometries. In particular, the case with the subsampled Fourier transform
finds applications to undersampled magnetic resonance imaging. In this talk, I will
show how the theory of compressed sensing can also be rigorously applied to the
sparse Radon transform, in which only a finite number of angles are considered. One
of the main novelties consists in the fact that the Radon transform is associated to
an ill-posed inverse problem, and the result follows from a new theory of compressed
sensing for abstract inverse problems. This is a joint work with G.S. Alberti, A. Felisi and
S.I. Trapasso.