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.

Date Published: 15 March 1994
PDF: 19 pages
Proc. SPIE 2242, Wavelet Applications, (15 March 1994); doi: 10.1117/12.170015

Published in SPIE Proceedings Vol. 2242:
Wavelet Applications
Harold H. Szu, Editor(s)