Analytical Fourier samples of spline-defined regions for pMRI reconstruction phantoms

Laurent Lejeune

Semester Project

Electrical and Electronics Engineering, EPFL

January 2010

Abstract

Analytical phantoms are synthetic shapes used in pMRI simulation to obtain measurements without resorting to numerical methods. The advantage of the analytical approach is that it allows one to obtain measurements that can be considered as ground-truth data. Also, the risks of committing an inverse crime is avoided thanks to this approach. From a theoretical point of view, generating measurements with phantoms boils down to solving a 2D continuous Fourier transform. In this project, we implemented a simulator that computes measurements for phantoms defined in a piecewise fashion using splines of order 1 (polygons) and 2 (Bezier-curves). The sensitivity profile was modelized in two different ways: Using 2D polynomials and the complex exponential basis.