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  "body": "\n## Summary\n\nFiltered back-projection is the standard method to reconstruct a function in the plane from its [[Radon transform|VJNZJ352PC]].\nIt has two steps.\nFirst each projection is convolved with a filter whose Fourier transform is close to $\\abs{\\sigma}$.\nThen the filtered projections are fed into the [[dual Radon transform|938SXZQS8G]].\nWith the exact ramp filter it is the [[Radon inversion formula|HN93ST5CBT]] in dimension $2$.\nPractical filters cut off high frequencies, and the method then reconstructs a smoothed version of the function.\nIt was for a long time the main algorithm of computed tomography scanners.\n\n## Explanations\n\n### L1 human\n\nBack-projection alone smears each measurement along its line and gives a blurred image.\nThe blur can be computed: it boosts low frequencies too much compared with high ones.\nSo before smearing back, each measured profile is filtered to undo this imbalance.\nThe filter sharpens the edges of each profile, and after back-projection the blur is gone.\n",
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