DIP Lecture 18 Reconstruction from parallel projections and the Radon transform

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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.).

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