| James Dow Allen 2008-01-03, 3:56 am |
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What journal article first noted the optimality of
nonunitary filter banks in subband coding?
IIRC the low-pass synthesis filter used in JPEG-2000 is
bell-shaped and looks much like a blurring filter. The
low-pass analysis filter has more of a Mexican-hat shape,
similar to a sharpening function.
IEEE Trans Image Proc'g, Dec 1995, has an article
"On the Optimality of Nonunitary Filter Banks in Subband
Coders",
by
Aase, S.O. and Ramstad, T.A.
IIRC it cites an earlier article by the same authors:
1993 Proceedings SPIE Still-image compression, pages V-566 to V-569.
Subband coding was well-known by 1993; surely the
non-orthogonality of optimal compaction coding
was already actively exploited, at least by some.
But was Aase's paper really the first to point the fact out?
(I'd guess many workers were surprised to learn of this
result. The Karhunen-Loeve Theorem guarantees orthogonality
for both block-based and general filter banks. Subband
coders are the special exception because, by their definition,
subband filters will overlap and have a finite bound
on the support size (length of transform vector).)
James D. Allen
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