A Fast Approximate Karhunen-Loève Transform (AKLT) for Data Compression

✍ Scribed by Irving S. Reed; Leu-Shing Lan

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 508 KB
• Volume: 5
• Category: Article
• ISSN: 1047-3203
• DOI: 10.1006/jvci.1994.1029

✦ Synopsis

The Karhunen-Loève transform 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-Loève 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. 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. 1994 Academic Press, tnc.