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Proceedings Paper

Fast approximate Karhunen-Loeve transform with applications to digital image coding
Author(s): Leu-Shing Lan; Irving S. Reed
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Paper Abstract

The Karhunen-Loeve transform (KLT) is known to be the optimal transform for data compression. However, since it is signal dependent and lacks a fast algorithm, it is not used in practice. In this paper, a fast approximate Karhunen-Loeve transform (AKLT) is presented. This new transform is derived using perturbation theory of linear operators. Both the forward and inverse AKLT are analytically derived in closed forms. In addition, fast computational algorithms are developed for both the forward and inverse transforms. The order of computational complexity for the AKLT is N log2 N, which is the same as that of the DCT, the transform presently used in industrial practice. Performance comparisons reveal for a first-order Markov sequence that the AKLT performs better than the DCT in its energy compaction and signal decorrelation capabilities. Experiments on real images also demonstrate a definite superiority of the AKLT over the DCT when an adaptive scheme is used.

Paper Details

Date Published: 22 October 1993
PDF: 12 pages
Proc. SPIE 2094, Visual Communications and Image Processing '93, (22 October 1993); doi: 10.1117/12.157962
Show Author Affiliations
Leu-Shing Lan, Univ. of Southern California (United States)
Irving S. Reed, Univ. of Southern California (United States)

Published in SPIE Proceedings Vol. 2094:
Visual Communications and Image Processing '93
Barry G. Haskell; Hsueh-Ming Hang, Editor(s)

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