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  "body": "\n## Summary\n\nThe X-ray transform sends a function $f$ on $\\R^n$ to the function that gives the integral of $f$ along each line.\nIn the plane it is the [[Radon transform|VJNZJ352PC]], up to the parametrization of lines.\nIn higher dimensions lines are smaller than hyperplanes, and the two transforms differ.\nIt models what X-ray tomography measures in three dimensions, where the data are line integrals.\nIt is injective on integrable functions, and in dimension $n \\ge 3$ the data are overdetermined, since the set of lines has dimension $2n - 2 \u003e n$.\n\n## Explanations\n\n### L1 human\n\nAn X-ray passes through a body along a straight line, and the detector measures the total density along that line.\nThe X-ray transform collects these totals for all lines.\nFor example, the integral of a ball of uniform density $1$ and radius $a$ along a line at distance $d \u003c a$ from the center is the chord length $2\\sqrt{a^2 - d^2}$.\nFrom all these totals one can recover the density, which is what three-dimensional scanners do.\n",
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