The Karhunen-Loeve, Discrete Cosine, and Related Transforms Obtained via the Hadamard Transform
Kansas State University
Ames Research Center, NASA
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AbstractThe Karhunen-Loeve transform for stationary data, the discrete cosine transform, the Walsh-Hadamard transform, and most other commonly used transforms have one-half even and one-half odd transform vectors. Such even/odd transforms can be implemented by following a Walsh-Hadamard transform by a sparse matrix multiplication, as previously reported by Hein and Ahmed for the discrete cosine transform. The discrete cosine transform provides data compression nearly equal to that of the Karhunen-Loeve transform, for the first order Markov correlation model. The Walsh-Hadamard transform provides most of the potential data compression for this correlation model, but it always provides less data compression than the discrete cosine transform. Even/odd transforms can be designed to approach the performance of the Karhunen-Loeve or discrete cosine transform, while meeting various restrictions which can simplify hardware implementation. The performance of some even/odd transforms is compared theoretically and experimentally. About one-half of the performance difference between the Walsh- Hadamard and the discrete cosine transforms is obtained by simple post-processing of the Walsh-Hadamard transform coefficients.
SponsorsInternational Foundation for Telemetering