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=== Preliminaries: parametrisation of a line in the plane === | === Preliminaries: parametrisation of a line in the plane === | ||
'''Q1:''' In a two-dimensional space, how many parameters are needed in order to define a line? Provide some examples of equations that uniquely define a line in the plane. | '''Q1:''' In a two-dimensional space, how many parameters are needed in order to define a line? Provide some examples of equations that uniquely define a line in the plane. | ||
[[File:Line_parametrisation.png |thumb|center| Parametrisation <math>(t,\Phi)</math> of a line in the plane.)]] | |||
Revision as of 21:22, 15 October 2021
Radon transform and X-ray tomography
The goal of this homework is to introduce the Radon transform of a two-dimensional function. We will show that this transform is invertible and the inverse involves the Fourier transform in two dimensions. From a practical point of view, the Radon transform is the basis of X-ray tomography (as well as X-ray scanning), applied in the medical context in order to obtain cross-section images of different organs. The second part of the homework consists of a documentation work to be conducted in pairs: each pair of students should prepare a blackboard presentation of approximately five minutes on this part.
Radon transform
Preliminaries: parametrisation of a line in the plane
Q1: In a two-dimensional space, how many parameters are needed in order to define a line? Provide some examples of equations that uniquely define a line in the plane.
