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  "body": "\n## Summary\n\nMatching pursuit is a greedy algorithm that builds an approximation of a vector from a dictionary of unit vectors, one element at a time.\nAt each step it picks the dictionary element most correlated with the current residual and removes the projection of the residual on that element.\nIt gives a cheap way to compute [[n-term approximations|GEK0NP5WQM]] and [[sparse approximations|WC8P971XGW]] when the exact problem is too hard.\nA variant, orthogonal matching pursuit, re-projects onto all chosen elements at each step.\n\n## Explanations\n\n### L1 human\n\nImagine explaining a sound with a few notes from a large catalogue.\nMatching pursuit first picks the note that matches the sound best, subtracts it, and then repeats with what is left.\nEach step makes the leftover part shorter, because a component of it is removed.\nIn $\\R^2$ with the dictionary $e_1$, $e_2$ and $u = (e_1 + e_2)/\\sqrt{2}$, the vector $f = (2, 1)$ first picks $u$, since $\\ip{f}{u} = 3/\\sqrt{2}$ is the largest correlation.\nThe leftover $(1/2, -1/2)$ then needs both $e_1$ and $e_2$, so the greedy method uses three elements, while $f = 2e_1 + e_2$ needs only two.\n",
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