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function c = fwt2(f,w,J,varargin)
%-*- texinfo -*-
%@deftypefn {Function} fwt2
%@verbatim
%FWT2 Fast Wavelet Transform 2D
% Usage: c = fwt2(f,w,J);
% c = fwt2(f,w,J,...);
%
% Input parameters:
% f : Input data.
% w : Wavelet filter bank definition.
% J : Number of filter bank iterations.
%
% Output parameters:
% c : Coefficients stored in a matrix.
%
% c=FWT2(f,w,J) returns wavelet coefficients c of the input matrix f*
% using J iterations of the basic wavelet filter bank defined by w.
% Please see FWT for description of w and J.
%
% FWT2 supports just the non-expansive boundary condition 'per' and
% critically subsampled filter banks in order to be able to pack the
% coefficients in a matrix. Also the J is limited to some maximum value
% for the same reason.
%
% Additional flags make it possible to specify how the algorithm
% should subdivide the matrix:
%
% 'standard'
% Standard behaviour of the JPEG 2000 standard.
% This is the default.
%
% 'tensor'
% This corresponds to doing a full FWT along each dimension of
% the matrix.
%
% Examples:
% ---------
%
% Some simple example of calling the FWT2 function, compare with the
% CAMERAMAN image. Only the 70 dB largest coefficients are shown, to
% make the structures more visible.
%
% The first example uses the standard layout:
%
% c = fwt2(cameraman,'db8',4);
% imagesc(dynlimit(20*log10(abs(c)),70));
% axis('image'); colormap(gray);
%
% The second example uses the tensor product layout:
%
% c = fwt2(cameraman,'db8',4,'tensor');
% imagesc(dynlimit(20*log10(abs(c)),70));
% axis('image'); colormap(gray);
%
%
%
% References:
% S. Mallat. A wavelet tour of signal processing. Academic Press, San
% Diego, CA, 1998.
%
%
%@end verbatim
%@strong{Url}: @url{http://ltfat.github.io/doc/wavelets/fwt2.html}
%@seealso{ifwt2, fwtinit, demo_imagecompression}
%@end deftypefn
% Copyright (C) 2005-2016 Peter L. Soendergaard <peter@sonderport.dk>.
% This file is part of LTFAT version 2.3.1
%
% This program is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program. If not, see <http://www.gnu.org/licenses/>.
% AUTHOR: Zdenek Prusa
if nargin<3
error('%s: Too few input parameters.',upper(mfilename));
end;
complainif_notposint(J,'J');
[M,N]=size(f);
if(M==1||N==1)
error('%s: The input data is vector.',upper(mfilename));
end
% Initialize the wavelet filters structure
w = fwtinit(w);
if(~all(w.a==length(w.h)))
error('%s: Non-critically subsampled filter banks not supported.',...
upper(mfilename));
end
%Do not allow single wavelet coefficient at two consecutive levels
if(any(w.a(1)^J>size(f)))
error(['%s: %d-level decomposition of the input is not possible. ',...
'Maximum J is %d.'],...
upper(mfilename),J,floor(log(min(size(f)))/log(w.a(1))));
end
%% ----- step 0 : Check inputs -------
definput.import = {'fwt2'};
[flags,kv]=ltfatarghelper({},definput,varargin);
nFilts = numel(w.h);
Lcrows = fwtclength(size(f,1),w,J);
Lccols = fwtclength(size(f,2),w,J);
if(flags.do_standard)
Jstep = 1;
c = fwt(f,w,Jstep,'dim',1,'per');
c = fwt(c,w,Jstep,'dim',2,'per');
for jj=1:J-1
colRange = 1:Lcrows(end-jj*(nFilts-1)+1);
rowRange = 1:Lccols(end-jj*(nFilts-1)+1);
c(colRange,rowRange) = fwt(c(colRange,rowRange),w,Jstep,'dim',1,'per');
c(colRange,rowRange) = fwt(c(colRange,rowRange),w,Jstep,'dim',2,'per');
end
elseif(flags.do_tensor)
c = fwt(f,w,J,'dim',1,'per');
c = fwt(c,w,J,'dim',2,'per');
else
error('%s: Should not get here. Bug somewhere else.',upper(mfilename));
end
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