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I have done similar work. looking at your problem statement, following would be my workflow:
1. ellipse problem: sample the ellipse on 256x256 grid using ellipse's equation and use use radon transform for getting projections, it will be followed by filtered backprojection of the radon transform
2. [login to view URL] part: First i will demonstrate reconstruction via backprojection, using 180 equispaced projections in [0,180] interval. Later filtered backprojection would be demonstrated for 258 projection case.