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=Radon transform and X-ray tomography= | =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 | 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. | 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. | |||
Revision as of 21:20, 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.