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  "body": "\n## Summary\n\nCurvelets are a multiscale system of functions on the plane that are indexed by scale, orientation and position.\nAt fine scales they are thin needles whose width is roughly the square of their length, a rule called parabolic scaling.\nThis shape matches smooth curves well, so images that are smooth apart from smooth edges have sparse curvelet expansions.\nFor such images, the best approximation with $N$ curvelets has squared error of order $N^{-2}(\\log N)^3$, while $N$ wavelets give only order $N^{-1}$.\n\n## Explanations\n\n### L1 human\n\nTwo-dimensional wavelets are small square blobs, so following a curved edge needs many of them.\nCurvelets are long, thin and oriented, like short strokes of a pen.\nA smooth edge, seen up close, is almost a straight segment, and a single curvelet aligned with it covers it.\nAs the scale gets finer, the strokes get thinner faster than they get shorter, and there are more possible directions.\nThis is why curvelets describe images with clean contours using far fewer terms than wavelets.\n",
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