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

[isaackleiner]

thanks a lot! I'm doing my degree project about radon transform, and this was absolutely helpful!

[javier]

Hey thanks for this. I guess that sqr(r) at 25:25 is actually r2 right?

[s.wiesinger]

Thank you very much! Your lecture was very helpful!

[trinetram]

Thank you sir for this lecture please provide some good reference books on the topic it would be very helpful thanking you again ❤️❤️❤️❤️

[adwait]

with music it do feel like a mathematical meditation