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I presented two multiscale methods for sparse data interpolation problems: multiscale
regularization and the quadtree pyramid. Multiscale regularization produced an order-of-magnitude
speedup (100 iterations versus 1000) in convergence for least squares interpolation of sparsely
sampled topographical data,
compared to regularization with a simple Laplacian. The quadtree pyramid produces a result which
is of decent quality, with essentially no cost - roughly one iteration. When used as a starting
guess for iterative solutions (simple Laplacian regularization), the quadtree pyramid result
leads to a good result for ten times fewer iterations.

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** Up:** Brown: Sparse data interpolation
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Stanford Exploration Project

9/5/2000