Wavelet approximations to Jacobians and the inversion of complicated maps

Mladen Victor Wickerhauser

doi:10.1117/12.170015

15 March 1994 Wavelet approximations to Jacobians and the inversion of complicated maps

Mladen Victor Wickerhauser

Proceedings Volume 2242, Wavelet Applications; (1994) https://doi.org/10.1117/12.170015
Event: SPIE's International Symposium on Optical Engineering and Photonics in Aerospace Sensing, 1994, Orlando, FL, United States

Abstract

Principal orthogonal decomposition can be used to solve two related problems: distinguishing elements from a collection by making d measurements, and inverting a complicated map from a p- parameter configuration space to a d-dimensional measurement space. In the case where d is more than 1000 or so, the classical O(d³) singular value decomposition algorithm becomes very costly, but it can be replaced with an approximate best-basis method that has complexity O(d² log d). This can be used to compute an approximate Jacobian for a complicated map from R^p to R^d in the case where p is much less than d.

Citation Download Citation

Mladen Victor Wickerhauser "Wavelet approximations to Jacobians and the inversion of complicated maps", Proc. SPIE 2242, Wavelet Applications, (15 March 1994); https://doi.org/10.1117/12.170015

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