Nonlinear improvement of Karhunen-Loeve bases obtained by approximate 2D procedures
Yurij S. Musatenko, Vitalij N. Kurashov · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1997
In this paper we suggest two new algorithms for improving approximate Karhunen-Loeve (KL) bases for image processing problems. One of them is an algorithm for finding the best 2D approximate KL basis, the second is a nonlinear 2D algorithm with previous image preparation. By 2D bases is meant the basis for which 2D-basis functions are obtained as a product of 1D-functions. We show that in such sense the best 2D basis for a given ensemble really exists, and we offer the procedure for its construction. The procedure is not fast, but in spite of this it permits to demonstrate that energy accumulation for such best basis in majority of cases is much worse than for true KL basis. Consequently, all fast 2D algorithms, such as wavelet-based algorithm of approximate KL transform, can not give sufficient energy accumulation. FOr the purpose to improve this situation we offer fast nonlinear procedure which reversibly transform image spatial properties in such a way that the processed ensemble has improved energy accumulation in KL bases obtained by above-mentioned fast algorithms of approximate KL transform.