1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
|
function f = ifwt(c,par,varargin)
%-*- texinfo -*-
%@deftypefn {Function} ifwt
%@verbatim
%IFWT Inverse Fast Wavelet Transform
% Usage: f = ifwt(c,info)
% f = ifwt(c,w,J,Ls)
% f = ifwt(c,w,J,Ls,dim)
%
% Input parameters:
% c : Wavelet coefficients.
% info,w : Transform parameters struct/Wavelet filters definition.
% J : Number of filterbank iterations.
% Ls : Length of the reconstructed signal.
% dim : Dimension to along which to apply the transform.
%
% Output parameters:
% f : Reconstructed data.
%
% f = IFWT(c,info) reconstructs signal f from the wavelet coefficients
% c using parameters from info struct. both returned by FWT
% function.
%
% f = IFWT(c,w,J,Ls) reconstructs signal f from the wavelet coefficients
% c using J*-iteration synthesis filterbank build from the basic
% filterbank defined by w. The Ls parameter is mandatory due to the
% ambiguity of lengths introduced by the subsampling operation and by
% boundary treatment methods. Note that the same flag as in the FWT
% function have to be used, otherwise perfect reconstruction cannot be
% obtained.
%
% In both cases, the fast wavelet transform algorithm (Mallat's algorithm)
% is employed. The format of c can be either packed, as returned by the
% FWT function or cell-array as returned by WAVPACK2CELL function.
%
% Please see the help on FWT for a detailed description of the parameters.
%
% Examples:
% ---------
%
% A simple example showing perfect reconstruction:
%
% f = gspi;
% J = 8;
% c = fwt(f,'db8',J);
% fhat = ifwt(c,'db8',J,length(f));
% % The following should give (almost) zero
% norm(f-fhat)
%
%
% 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/ifwt.html}
%@seealso{fwt, wavpack2cell, wavcell2pack}
%@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
complainif_notenoughargs(nargin,2,'IFWT');
if ~(iscell(c) || isnumeric(c)) || isempty(c)
error('%s: Unrecognized coefficient format.',upper(mfilename));
end
if(isstruct(par)&&isfield(par,'fname'))
complainif_toomanyargs(nargin,2,'IFWT');
if ~strcmpi(par.fname,'fwt')
error(['%s: Wrong func name in info struct. ',...
' The info parameter was created by %s.'],...
upper(mfilename),par.fname);
end
% process info struct
w = fwtinit({'dual',par.wt});
J = par.J;
Lc = par.Lc;
Ls = par.Ls;
dim = par.dim;
ext = par.ext;
L = fwtlength(Ls,w,J,ext);
else
complainif_notenoughargs(nargin,4,'IFWT');
%% PARSE INPUT
definput.import = {'fwt'};
definput.keyvals.dim = [];
definput.keyvals.Ls = [];
definput.keyvals.J = [];
[flags,~,J,Ls,dim]=ltfatarghelper({'J','Ls','dim'},definput,varargin);
complainif_notposint(J,'J');
complainif_notposint(Ls,'Ls');
ext = flags.ext;
%If dim is not specified use the first non-singleton dimension.
if(isempty(dim))
dim=find(size(c)>1,1);
else
if(~any(dim==[1,2]))
error('%s: Parameter *dim* should be 1 or 2.',upper(mfilename));
end
end
% Initialize the wavelet filters structure
w = fwtinit(par);
%% ----- Determine input data length.
L = fwtlength(Ls,w,J,ext);
%% ----- Determine number of ceoefficients in each subband
Lc = fwtclength(L,w,J,ext);
end
%% ----- Change c to correct shape according to the dim.
if(isnumeric(c))
%Check *Lc*
if(sum(Lc)~=size(c,dim))
error('%s: Coefficient subband lengths does not comply with parameter *Ls*.',upper(mfilename));
end
%Change format
c = wavpack2cell(c,Lc,dim);
elseif(iscell(c))
%Just check *Lc*
if(~isequal(Lc,cellfun(@(x) size(x,1),c)))
error('%s: Coefficient subband lengths does not comply with parameter *Ls*.',upper(mfilename));
end
else
error('%s: Unrecognized coefficient format.',upper(mfilename));
end;
%% ----- Run computation
f = comp_ifwt(c,w.g,w.a,J,L,ext);
f = postpad(f,Ls);
%% ----- FINALIZE: Reshape back according to the dim.
if(dim==2)
f = f.';
end
%END IFWT
|
