New perspectives on optimal transforms of random vectors

P. G. Howlett (), C. E. M. Pearce () and A. P. Torokhti ()
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P. G. Howlett: The University of South Australia
C. E. M. Pearce: The University of Adelaide
A. P. Torokhti: The University of South Australia

Chapter Chapter 13 in Optimization, 2009, pp 245-259 from Springer

Abstract: Abstract We present a new transform which is optimal over the class of transforms generated by second-degree polynomial operators. The transform is based on the solution of the best constrained approximation problem with the approximant formed by a polynomial operator. It is shown that the new transform has advantages over the Karhunen–Loève transform, arguably the most popular transform, which is optimal over the class of linear transforms of fixed rank. We provide a strict justification of the technique, demonstrate its advantages and describe useful extensions and applications.

Keywords: Optimal transforms; singular-value decomposition; filtering; compression; tensors; random signals (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-0-387-98096-6_13

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DOI: 10.1007/978-0-387-98096-6_13

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