Seventeen dubious methods to approximate the gradient for nonlinear filters with particle flow

Fred Daum; Jim Huang; Misha Krichman; Talia Kohen

doi:10.1117/12.823519

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4 September 2009 Seventeen dubious methods to approximate the gradient for nonlinear filters with particle flow

Fred Daum, Jim Huang, Misha Krichman, Talia Kohen

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Proceedings Volume 7445, Signal and Data Processing of Small Targets 2009; 74450V (2009) https://doi.org/10.1117/12.823519
Event: SPIE Optical Engineering + Applications, 2009, San Diego, California, United States

Abstract

We have investigated more than 17 distinct methods to approximate the gradient of the loghomotopy for nonlinear filters. This is a challenging problem because the data are given as function values at random points in high dimensional space. This general problem is important in optimization, financial engineering, quantum chemistry, chemistry, physics and engineering. The best general method that we have developed so far uses a simple idea borrowed from geology combined with a fast approximate k-NN algorithm. Extensive numerical experiments for five classes of problems shows that we get excellent performance.

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Fred Daum, Jim Huang, Misha Krichman, and Talia Kohen "Seventeen dubious methods to approximate the gradient for nonlinear filters with particle flow", Proc. SPIE 7445, Signal and Data Processing of Small Targets 2009, 74450V (4 September 2009); https://doi.org/10.1117/12.823519

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