Two strategies for sparse data interpolation

Morgan Brown

morgan@sep.stanford.edu

ABSTRACT

I introduce two strategies to overcome the slow convergence of least squares sparse data interpolation: 1) a 2-D multiscale Laplacian regularization operator, and 2) an explicit quadtree-style upsampling scheme which produces a good initial guess for iterative schemes. The multiscale regularization produces an order-of-magnitude speedup in the interpolation of a sparsely sampled topographical map. The quadtree method produces an initial guess which leads to similar speedups for iterative methods.