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function f=iuwpfbt(c,par,varargin)
%-*- texinfo -*-
%@deftypefn {Function} iuwpfbt
%@verbatim
%IUWPFBT Inverse Undecimated Wavelet Packet Filterbank Tree
% Usage: f=iuwpfbt(c,info);
% f=iuwpfbt(c,wt);
%
% Input parameters:
% c : Coefficients stored in L xM matrix.
% info,wt : Transform parameters struct/Wavelet tree definition.
%
% Output parameters:
% f : Reconstructed data.
%
% f = IUWPFBT(c,info) reconstructs signal f from the wavelet packet
% coefficients c using parameters from info struct. both returned by
% the UWPFBT function.
%
% f = IUWPFBT(c,wt) reconstructs signal f from the wavelet packet
% coefficients c using the undecimated wavelet filterbank tree
% described by wt.
%
% Please see help for WFBT description of possible formats of wt.
%
% Filter scaling:
% ---------------
%
% As in UWPFBT, the function recognizes three flags controlling scaling
% of filters:
%
% 'sqrt'
% Each filter is scaled by 1/sqrt(a), there a is the hop
% factor associated with it. If the original filterbank is
% orthonormal, the overall undecimated transform is a tight
% frame.
% This is the default.
%
% 'noscale'
% Uses filters without scaling.
%
% 'scale'
% Each filter is scaled by 1/a.
%
% If 'noscale' is used, 'scale' must have been used in UWPFBT (and vice
% versa) in order to obtain a perfect reconstruction.
%
% Scaling of intermediate outputs:
% --------------------------------
%
% The following flags control scaling of the intermediate coefficients.
% The intermediate coefficients are outputs of nodes which ale also
% inputs to nodes further in the tree.
%
% 'intsqrt'
% Each intermediate output is scaled by 1/sqrt(2).
% If the filterbank in each node is orthonormal, the overall
% undecimated transform is a tight frame.
% This is the default.
%
% 'intnoscale'
% No scaling of intermediate results is used.
%
% 'intscale'
% Each intermediate output is scaled by 1/2.
%
% If 'intnoscale' is used, 'intscale' must have been used in UWPFBT
% (and vice versa) in order to obtain a perfect reconstruction.
%
% Examples:
% ---------
%
% A simple example showing perfect reconstruction using the "full
% decomposition" wavelet tree:
%
% f = greasy;
% J = 7;
% wtdef = {'db10',J,'full'};
% c = uwpfbt(f,wtdef);
% fhat = iuwpfbt(c,wtdef);
% % The following should give (almost) zero
% norm(f-fhat)
%
%
%@end verbatim
%@strong{Url}: @url{http://ltfat.github.io/doc/wavelets/iuwpfbt.html}
%@seealso{wfbt, wfbtinit}
%@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/>.
complainif_notenoughargs(nargin,2,'IUWPFBT');
if isempty(c) || ~isnumeric(c)
error('%s: Unrecognized coefficient format.',upper(mfilename));
end
if(isstruct(par)&&isfield(par,'fname'))
complainif_toomanyargs(nargin,2,'IUWPFBT');
if ~strcmpi(par.fname,'uwpfbt')
error(['%s: Wrong func name in info struct. The info parameter ',...
'was created by %s.'],upper(mfilename),par.fname);
end
wt = wfbtinit({'dual',par.wt},par.fOrder);
scaling = par.scaling;
interscaling = par.interscaling;
% Use the "oposite" scaling of intermediate node outputs
if strcmp(interscaling,'intscale')
interscaling = 'intnoscale';
elseif strcmp(interscaling,'intnoscale')
interscaling = 'intscale';
end
% Use the "oposite" scaling of filters
if strcmp(scaling,'scale')
scaling = 'noscale';
elseif strcmp(scaling,'noscale')
scaling = 'scale';
end
else
definput.import = {'wfbtcommon','uwfbtcommon'};
definput.flags.interscaling = {'intsqrt', 'intscale', 'intnoscale'};
[flags]=ltfatarghelper({},definput,varargin);
scaling = flags.scaling;
interscaling = flags.interscaling;
% Initialize the wavelet tree structure
wt = wfbtinit(par,flags.forder);
end
wtPath = fliplr(nodeBForder(0,wt));
[pOutIdxs,chOutIdxs] = treeWpBFrange(wt);
nodesUps = nodesFiltUps(wtPath,wt);
f = comp_iuwpfbt(c,wt.nodes(wtPath),nodesUps,pOutIdxs,chOutIdxs,scaling,...
interscaling);
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