Tomography - Lecture 2 - The Radon Transform скачать в хорошем качестве

Tomography - Lecture 2 - The Radon Transform

In this lecture we introduce the Radon transform, and we examine several properties, such as shifting and scaling. We develop exact formulas for the sinograms of ellipses and circles which can be used later to give precise descriptions of the sinograms determined from the Radon transform of phantoms. Errata: at 25:40 it should be R^2 Music: Flames by Dan Henig Flowers in Heaven by Craig Hardgrove Chomber by Craig Hardgrove Dude by Patrick Patrikios Guardians + Tek by Craig Hardgrove 0:00 Start 6:26 Whiteboard Start - Radon Transform Definition 14:26 Example 1 - Radon Transform of an off center Circle 23:37 Example 2 - Radon Transform of a Circle of Radius R 33:38 Example 3 - Square 40:30 Example 4 - Cone 45:25 Properties of the Laplace Transform - Linearity 47:42 Example 5 - Linearity Example 50:42 Shifting Property 56:40 Example 6 - Shifting Example 58:18 Scaling Property 1:02:15 Phantoms 1:04:50 Radon Transform of an Ellipse 1:14:32 Closing Remarks