Entropy Encoding, Hilbert Space and Karhunen-Loeve Transforms
Palle E. T. Jorgensen, Myung-Sin Song
TL;DR
This paper introduces a mathematical framework using Hilbert spaces and operators to improve entropy encoding and data approximation, providing precise formulas and optimal orthogonal bases for data encoding.
Contribution
It presents a novel approach combining Hilbert space theory with entropy encoding to derive optimal orthogonal bases for data approximation and compression.
Findings
Derived formulas for entropy encoding in Hilbert space
Established orthogonal bases optimizing data encoding measures
Provided quantitative estimates for data approximation
Abstract
By introducing Hilbert space and operators, we show how probabilities, approximations and entropy encoding from signal and image processing allow precise formulas and quantitative estimates. Our main results yield orthogonal bases which optimize distinct measures of data encoding.
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