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function x = idddtree2(dt)
%IDDDTREE2 Inverse Real and Complex Double and Double-Density
% Dual-Tree 2-D DWT
% X = IDDDTREE2(DT) returns the reconstructed matrix X
% using the decomposition tree DT.
%
% DT is a structure which contains five fields:
% type: type of tree.
% level: level of decomposition.
% filters: the filters for decomposition.
% cfs: coefficients of wavelet transform.
% sizes: sizes of components.
% See DDDTREE2 for more precision about the tree structure.
%
% The reconstruction filters FRf and Rf are included in
% the structure DT.
% FRf and Rf are cell arrays of vectors with:
% FRf{k}: First stage filters for tree k (k = 1,2)
% Rf{k} : Filters for remaining stages on tree k
%
% See also DDDTREE2, DDDTREE, DTFILTERS.
% M. Misiti, Y. Misiti, G. Oppenheim, J.M. Poggi 09-Nov-2012.
% Last Revision: 11-Mar-2013.
% Copyright 1995-2013 The MathWorks, Inc.
cfs = dt.cfs;
typetree = dt.type;
L = dt.level;
FRf = dt.filters.FRf;
Rf = dt.filters.Rf;
switch typetree
case 'dwt'
% Inverse 2-D Discrete Wavelet Transform
x = cfs{L+1};
for j = L:-1:1
x = recFB(x,cfs{j},Rf,Rf);
end
case 'realdt'
% Inverse 2-D Dual-Tree Discrete Wavelet Transform
% sum and difference
for j = 1:L
for m = 1:3
A = cfs{j}(:,:,m,1);
B = cfs{j}(:,:,m,2);
cfs{j}(:,:,m,1) = (A+B)/sqrt(2);
cfs{j}(:,:,m,2) = (A-B)/sqrt(2);
end
end
% Tree 1 and Tree 2
x = 0;
for k = 1:2
y = cfs{L+1}(:,:,k);
for j = L:-1:1
if j==1 , recFILT = FRf{k}; else recFILT = Rf{k}; end
y = recFB(y,cfs{j}(:,:,:,k),recFILT);
end
x = x+y;
end
x = x/sqrt(2);
case 'cplxdt'
% Inverse 2-D Dual-Tree Complex Discrete Wavelet Transform
for j = 1:L
for m = 1:3
A = cfs{j}(:,:,m,1,1);
B = cfs{j}(:,:,m,2,2);
cfs{j}(:,:,m,1,1) = (A+B)/sqrt(2);
cfs{j}(:,:,m,2,2) = (A-B)/sqrt(2);
A = cfs{j}(:,:,m,2,1);
B = cfs{j}(:,:,m,1,2);
cfs{j}(:,:,m,2,1) = (A+B)/sqrt(2);
cfs{j}(:,:,m,1,2) = (A-B)/sqrt(2);
end
end
x = 0;
for k = 1:2
for n = 1:2
y = cfs{L+1}(:,:,n,k);
for j = L:-1:1
if j==1
recF1 = FRf{k}; recF2 = FRf{n};
else
recF1 = Rf{k}; recF2 = Rf{n};
end
y = recFB(y,cfs{j}(:,:,:,n,k),recF1,recF2);
end
x = x + y;
end
end
% normalization
x = x/2;
case 'ddt'
% Inverse 2-D Double-Density Discrete Wavelet Transform
x = cfs{L+1};
for j = L:-1:1
x = recFB3(x,cfs{j},FRf,Rf);
end
case 'realdddt'
% Inverse Real 2-D Double-Density Dual-Tree DWT
% sum and difference
for j = 1:L
for m = 1:8
A = cfs{j}(:,:,m,1);
B = cfs{j}(:,:,m,2);
cfs{j}(:,:,m,1) = (A+B)/sqrt(2);
cfs{j}(:,:,m,2) = (A-B)/sqrt(2);
end
end
% Tree 1 and 2
x = 0;
for k = 1:2
y = cfs{L+1}(:,:,k);
for j = L:-1:1
if j==1 , recFILT = FRf{k}; else recFILT = Rf{k}; end
y = recFB3(y,cfs{j}(:,:,:,k),recFILT);
end
x = x+y;
end
% normalization
x = x/sqrt(2);
case 'cplxdddt'
for j = 1:L
for n = 1:2
for m = 1:8
A = cfs{j}(:,:,m,n,1);
B = cfs{j}(:,:,m,n,2);
cfs{j}(:,:,m,n,1) = (A+B)/sqrt(2);
cfs{j}(:,:,m,n,2) = (A-B)/sqrt(2);
end
end
end
x = 0;
for k = 1:2
for n = 1:2
Lo = cfs{L+1}(:,:,n,k);
for j = L:-1:1
if j==1
recF1 = FRf{k}; recF2 = FRf{n};
else
recF1 = Rf{k}; recF2 = Rf{n};
end
Lo = recFB3(Lo,cfs{j}(:,:,:,n,k),recF1,recF2);
end
x = x + Lo;
end
end
% normalization
x = x/2;
end
%-------------------------------------------------------------------------
function x = recFB(Lo,Hi,Rf1,Rf2)
% 2D Reconstruction Filter Bank
%
% INPUT:
% Lo,Hi - lowpass,highpass subbands
% Rf1 - Reconstruction filters for the columns
% Rf2 - Reconstruction filters for the rows
% OUTPUT:
% x - output array
if nargin < 4 ,Rf2 = Rf1; end
% filter along rows
Lo = local_REC_FB(Lo,Hi(:,:,1),Rf2,2);
Hi = local_REC_FB(Hi(:,:,2),Hi(:,:,3),Rf2,2);
% filter along columns
x = local_REC_FB(Lo,Hi,Rf1,1);
%-------------------------------------------------------------------------
function x = local_REC_FB(Lo,Hi,Rf,d)
% 2D Reconstruction Filter Bank (along single dimension only)
%
% Rf - Reconstruction filters
% d - dimension of filtering
lpf = Rf(:,1); % lowpass filter
hpf = Rf(:,2); % highpass filter
if d == 2 , Lo = Lo'; Hi = Hi'; end
N = 2*size(Lo,1);
lf = length(Rf);
x = conv2(dyadup(Lo,0,'r'),lpf) + conv2(dyadup(Hi,0,'r'),hpf);
x(1:lf-2,:) = x(1:lf-2,:) + x(N+(1:lf-2),:);
x = x(1:N,:);
x = wshift('2d',x,[lf/2-1 0]);
if d == 2 , x = x'; end
%-------------------------------------------------------------------------
function x = recFB3(Lo,Hi,Rf1,Rf2)
% 2-D Reconstruction Filter Bank
%
% INPUT:
% Lo - lowpass subband
% Hi - ND array containing eight highpass subbands
% Rf1 - Reconstruction filters for the columns
% Rf2 - Reconstruction filters for the rows
if nargin < 4 , Rf2 = Rf1; end
% filter along rows
Lr = Rfb3_2D_A(Lo,Hi(:,:,1),Hi(:,:,2),Rf2,2);
H1r = Rfb3_2D_A(Hi(:,:,3),Hi(:,:,4),Hi(:,:,5),Rf2,2);
H2r = Rfb3_2D_A(Hi(:,:,6),Hi(:,:,7),Hi(:,:,8),Rf2,2);
% filter along columns
x = Rfb3_2D_A(Lr,H1r,H2r,Rf1,1);
%--------------------------------------------------------------------------
function x = Rfb3_2D_A(Lo,H1,H2,Rf,d)
% 2-D Reconstruction Filter Bank (along one dimension only)
%
% INPUT:
% Lo,H1,H2 - one lowpass and two highpass subbands
% Rf - Reconstruction filters
% d - dimension of filtering
Rlpf = Rf(:,1); % lowpass filter
Rhpf1 = Rf(:,2); % first highpass filter
Rhpf2 = Rf(:,3); % second highpass filter
if d == 2
Lo = Lo'; H1 = H1'; H2 = H2';
end
N = 2*size(Lo,1);
len = length(Rf);
x = conv2(dyadup(Lo,0,'r'),Rlpf) + conv2(dyadup(H1,0,'r'),Rhpf1) + ...
conv2(dyadup(H2,0,'r'),Rhpf2);
x(1:len-2,:) = x(1:len-2,:) + x(N+(1:len-2),:);
x = x(1:N,:);
x = wshift('2d',x,[len/2-1 0]);
if d == 2 ,x = x'; end
%-------------------------------------------------------------------------