DIP Lecture 18: Reconstruction from parallel projections and the Radon transform

ECSE-4540 Intro to Digital Image Processing
Rich Radke, Rensselaer Polytechnic Institute
Lecture 18: Reconstruction from parallel projections and the Radon transform (4/13/15)
0:00:07 Introduction to image reconstruction from projections
0:01:05 CT scan geometries
0:04:31 Parallel-beam projections
0:06:48 The idea of backprojection
0:08:20 Matlab example of projection and backprojection
0:14:22 Why is backprojection suboptimal?
0:16:36 Geometry and notation of projections
0:20:33 The Radon transform
0:23:26 The sinogram
0:26:50 Mathematics of backprojection
0:30:16 Adding up backprojections
0:31:57 The Fourier-Slice theorem
0:38:48 The idea of the theorem
0:41:45 Why the sum of backprojections is fuzzy (oversampling low frequencies)
0:44:16 Filtered backprojection
0:53:13 Summarizing the overall algorithm
0:56:29 Matlab FBP example
1:01:54 FBP in the spatial domain
1:05:02 Practical notes
Follows Section 5.11 of the textbook (Gonzalez and Woods, 3rd ed.).