## View abstract

### Session S08 - Inverse Problems and Applications

Friday, July 23, 17:00 ~ 17:30 UTC-3

## Inversion from a random sampling of the Radon transform in the context of LCA groups

### Erika Porten

#### Universidad Nacional de San Martín , Argentina   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak15931317283a2caa27404e521f177673').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy15931317283a2caa27404e521f177673 = '&#101;r&#105;k&#97;p&#111;rt&#101;n' + '&#64;'; addy15931317283a2caa27404e521f177673 = addy15931317283a2caa27404e521f177673 + 'gm&#97;&#105;l' + '&#46;' + 'c&#111;m'; var addy_text15931317283a2caa27404e521f177673 = '&#101;r&#105;k&#97;p&#111;rt&#101;n' + '&#64;' + 'gm&#97;&#105;l' + '&#46;' + 'c&#111;m';document.getElementById('cloak15931317283a2caa27404e521f177673').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy15931317283a2caa27404e521f177673 + '\'>'+addy_text15931317283a2caa27404e521f177673+'<\/a>';

Based on the definition of the Fourier transform on a locally compact abelian group $G$, we consider the problem of reconstructing a measurable function over $G$ from a countable subset of random samples. The sampling is carried out according to a Poisson random point process. For the interpolation step, we propose an iterative procedure in which a resampling is performed at each iteration, and we present error estimates of the approximation obtained. We apply these results to the problem of approximating the inverse Radon transform of a function. Finally, we present numerical simulations that support the effectiveness of the method.

Joint work with Marcela Morvidone (Universidad de San Martin, Argentina) and Juan Miguel Medina (Universidad de Buenos Aires, Argentina).