fwt2   

 fwt2.m

 Fast 2D wavelet transform.

 Usage: w = fwt(x, h0, h1, J, sym);
 x - mxn input image (min(m,n) must be divisible by 2^J) 
 h0 - lowpass decomposition filter
 h1 - highpass decomposition filter
      h0 and h1 should be zero padded appropriately so that they have the
      same length, and this length is even.
 J - number of levels in the filter bank.
     Right now, it must be chosen so that n*2^(-J) >= length(h0)
 sym - How to extend the input.
     sym=0: periodization
     sym=1: type-I symmetric extension ( [... x(2) x(1) x(2) x(3) ...])
            The wavelet filters must have type-I even symmetry 
            (e.g. daub79)
     sym=2: type-II symmetric extension ( [... x(2) x(1) x(1) x(2) x(3) ...])
            The lowpass filter must have type-II even symmetry, 
            The highpass filter must have type-II odd symmetry.
            (e.g. daub1018)

0001 % fwt2.m
0002 %
0003 % Fast 2D wavelet transform.
0004 %
0005 % Usage: w = fwt(x, h0, h1, J, sym);
0006 % x - mxn input image (min(m,n) must be divisible by 2^J)
0007 % h0 - lowpass decomposition filter
0008 % h1 - highpass decomposition filter
0009 %      h0 and h1 should be zero padded appropriately so that they have the
0010 %      same length, and this length is even.
0011 % J - number of levels in the filter bank.
0012 %     Right now, it must be chosen so that n*2^(-J) >= length(h0)
0013 % sym - How to extend the input.
0014 %     sym=0: periodization
0015 %     sym=1: type-I symmetric extension ( [... x(2) x(1) x(2) x(3) ...])
0016 %            The wavelet filters must have type-I even symmetry
0017 %            (e.g. daub79)
0018 %     sym=2: type-II symmetric extension ( [... x(2) x(1) x(1) x(2) x(3) ...])
0019 %            The lowpass filter must have type-II even symmetry,
0020 %            The highpass filter must have type-II odd symmetry.
0021 %            (e.g. daub1018)
0022 %
0023 
0024 %    2D Example's  output and explanation:
0025 %
0026 %       The coefficients in w are arranged as follows.
0027 %
0028 %              .------------------.
0029 %              |         |        |
0030 %              |    0    |   1    |
0031 %              |         |        |
0032 %              |   L,L   |   H,L  |
0033 %              |         |        |
0034 %              --------------------
0035 %              |         |        |
0036 %              |    2    |   3    |
0037 %              |         |        |
0038 %              |   L,H   |  H,H   |
0039 %              |         |        |
0040 %              `------------------'
0041 %
0042 %       where
0043 %            0 : Low pass vertically and Low pass horizontally
0044 %                (scaling coefficients)
0045 %            1 : Low pass vertically and high pass horizontally
0046 %            2 : High pass vertically and low  pass horizontally
0047 %            3 : High pass vertically and high pass horizontally
0048 %
0049 %
0050 % Written by: Justin Romberg
0051 % Created: April 2007
0052 
0053 % Modified by: Salman Asif
0054 %              December 2011
0055 % Added the ability to work with non-square images.
0056 % The only requirement is that min(ROW,COL) should be dyadic upto the
0057 % chosen scale J