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  "body": "\n## Summary\n\nAn inverse problem asks for the causes of observed effects: to recover the parameters of a model from measured data that the model produces.\nThe forward problem goes the other way and computes the data from known parameters.\nInverse problems are often ill-posed in the sense of Hadamard: small errors in the data can cause large errors in the answer.\nSo they need regularization.\nExamples are medical imaging, seismic exploration of the Earth, and the [[Calderón problem|R8Y8DDTWBM]].\n\n## Explanations\n\n### L1 human\n\nA doctor sees a CT scan, but the scanner only measures how much X-ray light passes through the body along many lines.\nTurning those line measurements back into a picture of the inside is an inverse problem.\nThe forward direction, from body to measurements, is easy and stable.\nThe inverse direction can magnify noise: two very different pictures may give almost the same measurements.\nA small example: knowing a function $y$, find $x = y'$; a tiny wiggle in $y$ can produce a huge wiggle in its derivative.\n",
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