In the following discussion (and the code in this subdirectory) the
analysis basis is called A, and is biorthogonal to the synthesis
basis, G. 

The analysis and synthesis bases need to be built to support a
specific image size.  The matlab m files found here can be used to
build these matrices.  Descriptions of each file can be found in
their headers or by typing help in matlab (e.g. >> help svdinvert). 

For square images of dimensions NxN, use GenBasis.m to generate a G
(synthesis) matrix and an A (analysis) matrix and use them as follows: 

Forward Transform (Analysis):
     C = A' I A

Inverse Transform (Synthesis):
     I = G  C G'

where C is the coefficient matrix and I is the image.

If the image is not square, but rather it has N rows  and M columns,
use GenBasis.m to generate two G matrices, Gn using dim=n and Gm using 
dim=m.  If you name the resulting analysis matrices An and Am, then
you use them as follows: 

C = An' I Am
I = Gn  C Gm'