Fast approximate Karhunen-Loeve transform with applications to digital image coding

Leu-Shing Lan; Irving S. Reed

doi:10.1117/12.157962

22 October 1993 Fast approximate Karhunen-Loève transform with applications to digital image coding

Leu-Shing Lan, Irving S. Reed

Proceedings Volume 2094, Visual Communications and Image Processing '93; (1993) https://doi.org/10.1117/12.157962
Event: Visual Communications and Image Processing '93, 1993, Cambridge, MA, United States

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.

Citation Download Citation

Leu-Shing Lan and Irving S. Reed "Fast approximate Karhunen-Loève transform with applications to digital image coding", Proc. SPIE 2094, Visual Communications and Image Processing '93, (22 October 1993); https://doi.org/10.1117/12.157962

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