The Distributed, Partial, And Conditional Karhunen-Loève Transforms

Authors:
Michael Gastpar;Pier-Luigi Dragotti;Martin Vetterli
Affiliations:
-;-;-
Venue:
DCC '03 Proceedings of the Conference on Data Compression
Year:
2003

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Abstract

The Karhunen-Loève transform (KLT) is a key element of many signal processing tasks, including approximation, compression, and classification. Manyrecent applications involve distributed signal processing where it is not generallypossible to apply the KLT to the signal; rather, the KLT must be approximatedin a distributed fashion. This paper investigates such distributed approximations to the KLT. First, we present explicit solutions to special cases, includinga partial KLT (where only a subset of the sources is observed), a conditionalKLT (where some sources act as side information), and the combination of thesetwo special cases. These results are used to derive an algorithm that finds thebest distributed approximation to the KLT.Applications of our results to sensor networks and to distributed databasesare discussed.