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Partly based on the ECE 637 material of Professor Bouman. | Partly based on the ECE 637 material of Professor Bouman. | ||
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| − | = | + | =Introduction= |
| + | The Fourier Slice Theorem elucidates how the projections measured by a medical imaging device can be used to reconstruct the object being scanned. From those projections a Continuous Time Fourier Transform (CTFT) is taken. Then according to the theorem, an inverse Continuous Space Fourier Transform (CSFT) can be used to form the original object,<math>f(x,y)</math>. There are two proofs that will be demonstrated. | ||
| + | =Fourier Slice Theorem= | ||
Put your content here . . . | Put your content here . . . | ||
Revision as of 11:39, 18 December 2014
Fourier Slice Theorem (FST)
A slecture by ECE student Sahil Sanghani
Partly based on the ECE 637 material of Professor Bouman.
Introduction
The Fourier Slice Theorem elucidates how the projections measured by a medical imaging device can be used to reconstruct the object being scanned. From those projections a Continuous Time Fourier Transform (CTFT) is taken. Then according to the theorem, an inverse Continuous Space Fourier Transform (CSFT) can be used to form the original object,$ f(x,y) $. There are two proofs that will be demonstrated.
Fourier Slice Theorem
Put your content here . . .
References:
[1] C. A. Bouman. ECE 637. Class Lecture. Digital Image Processing I. Faculty of Electrical Engineering, Purdue University. Spring 2013.
