brendt.wohlberg.net

Brendt Wohlberg and Chris Brislawn, "Symmetric Extension for Lifted Filter Banks and
Obstructions to Reversible Implementation", *Signal Processing*, vol. 88, no. 1, doi:10.1016/j.sigpro.2007.07.010, pp. 131--145, Jan 2008

Symmetric pre-extension is a standard approach to boundary
handling for finite-length input vectors with linear phase
filter banks. It works with both conventional linear
implementations and so-called *reversible*,
or integer-to-integer, implementations of odd-length linear
phase (*whole-sample symmetric*) filter
banks. In comparison, significant difficulties arise when using
symmetric pre-extension on reversible filter banks with
*even*-length (*half-sample
symmetric*) linear phase filters. An alternative
approach is presented using *lifting step
extension*, in which boundary extensions are performed
in each step of a lifting factorization, that avoids some of
these difficulties while preserving reversibility and retaining
the nonexpansive property of symmetric pre-extension. Another
alternative that is capable of preserving both reversibility and
subband symmetry for half-sample symmetric filter banks is
developed based on ideas from the theory of lattice vector
quantization. The practical ramifications of this work are
illustrated by describing its influence on the specification of
filter bank algorithms in Part 2 of the ISO/IEC JPEG 2000 image
coding standard.

@article{wohlberg-2007-symmetric,

author = {Brendt Wohlberg and Chris Brislawn},

title = {Symmetric Extension for Lifted Filter Banks and
Obstructions to Reversible Implementation},

year = {2008},

month = Jan,

urlpdf = {http://brendt.wohlberg.net/publications/pdf/wohlberg-2007-symmetric.pdf},

journal = {Signal Processing},

volume = {88},

number = {1},

doi = {10.1016/j.sigpro.2007.07.010},

pages = {131--145}

}