Hi...
This is prida thabah doing my MS in Medical Software..... Right now i am working on 5/3 and 9/7 filters, in this i have understand the logic of it. But, regarding the Lifting Scheme on this code i have few doubt, i want to know how they have used the Right shift , filters and Extrapolatedodd.
Please can you glance my code and reply me how is working.
My mail id is <snip email>
function X = waveletcdf97(X, Level)
%WAVELETCDF97 Cohen-Daubechies-Feauveau 9/7 wavelet transform.
% Y = WAVELETCDF97(X, L) decomposes X with L stages of the
% Cohen-Daubechies-Feauveau (CDF) 9/7 wavelet. For the
% inverse transform, WAVELETCDF97(X, -L) inverts L stages.
% Filter boundary handling is half-sample symmetric.
%
% X may be of any size; it need not have size divisible by 2^L.
% For example, if X has length 9, one stage of decomposition
% produces a lowpass subband of length 5 and a highpass subband
% of length 4. Transforms of any length have perfect
% reconstruction (exact inversion).
%
% If X is a matrix, WAVELETCDF97 performs a (tensor) 2D wavelet
% transform. If X has three dimensions, the 2D transform is
% applied along the first two dimensions.
%
% Example:
% Y = waveletcdf97(X, 5); % Transform image X using 5 stages
% R = waveletcdf97(Y, -5); % Reconstruct from Y
% Pascal Getreuer 2004-2006
if nargin < 2, error('Not enough input arguments.'); end
if ndims(X) > 3, error('Input must be a 2D or 3D array.'); end
if any(size(Level) ~= 1), error('Invalid transform level.'); end
N1 = size(X,1);
N2 = size(X,2);
% Lifting scheme filter coefficients for CDF 9/7
LiftFilter = [-1.5861343420693648,-0.0529801185718856,0.8829110755411875,0.4435068520511142];
ScaleFactor = 1.1496043988602418;
S1 = LiftFilter(1);
S2 = LiftFilter(2);
S3 = LiftFilter(3);
ExtrapolateOdd = -2*[S1*S2*S3,S2*S3,S1+S3+3*S1*S2*S3]/(1+2*S2*S3);
LiftFilter = LiftFilter([1,1],:);
if Level >= 0 % Forward transform
for k = 1:Level
M1 = ceil(N1/2);
M2 = ceil(N2/2);
%%% Transform along columns %%%
if N1 > 1
RightShift = [2:M1,M1];
X0 = X(1:2:N1,1:N2,:);
% Apply lifting stages
if rem(N1,2)
X1 = [X(2:2:N1,1:N2,:);X0(M1-1,:,:)*ExtrapolateOdd(1)...
+ X(N1-1,1:N2,:)*ExtrapolateOdd(2)...
+ X0(M1,:,:)*ExtrapolateOdd(3)]...
+ filter(LiftFilter(:,1),1,X0(RightShift,:,:),...
X0(1,:,:)*LiftFilter(1,1),1);
else
X1 = X(2:2:N1,1:N2,:) ...
+ filter(LiftFilter(:,1),1,X0(RightShift,:,:),...
X0(1,:,:)*LiftFilter(1,1),1);
end
X0 = X0 + filter(LiftFilter(:,2),1,...
X1,X1(1,:,:)*LiftFilter(1,2),1);
X1 = X1 + filter(LiftFilter(:,3),1,...
X0(RightShift,:,:),X0(1,:,:)*LiftFilter(1,3),1);
X0 = X0 + filter(LiftFilter(:,4),1,...
X1,X1(1,:,:)*LiftFilter(1,4),1);
if rem(N1,2)
X1(M1,:,:) = [];
end
X(1:N1,1:N2,:) = [X0*ScaleFactor;X1/ScaleFactor];
end
%%% Transform along rows %%%
if N2 > 1
RightShift = [2:M2,M2];
X0 = permute(X(1:N1,1:2:N2,:),[2,1,3]);
% Apply lifting stages
if rem(N2,2)
X1 = permute([X(1:N1,2:2:N2,:),X(1:N1,N2-2,:)*ExtrapolateOdd(1)...
+ X(1:N1,N2-1,:)*ExtrapolateOdd(2) ...
+ X(1:N1,N2,:)*ExtrapolateOdd(3)],[2,1,3])...
+ filter(LiftFilter(:,1),1,X0(RightShift,:,:),...
X0(1,:,:)*LiftFilter(1,1),1);
else
X1 = permute(X(1:N1,2:2:N2,:),[2,1,3]) ...
+ filter(LiftFilter(:,1),1,X0(RightShift,:,:),...
X0(1,:,:)*LiftFilter(1,1),1);
end
X0 = X0 + filter(LiftFilter(:,2),1,...
X1,X1(1,:,:)*LiftFilter(1,2),1);
X1 = X1 + filter(LiftFilter(:,3),1,...
X0(RightShift,:,:),X0(1,:,:)*LiftFilter(1,3),1);
X0 = X0 + filter(LiftFilter(:,4),1,...
X1,X1(1,:,:)*LiftFilter(1,4),1);
if rem(N2,2)
X1(M2,:,:) = [];
end
X(1:N1,1:N2,:) = permute([X0*ScaleFactor;X1/ScaleFactor],[2,1,3]);
end
N1 = M1;
N2 = M2;
end
else % Inverse transform
for k = 1+Level:0
M1 = ceil(N1*pow2(k));
M2 = ceil(N2*pow2(k));
%%% Inverse transform along rows %%%
if M2 > 1
Q = ceil(M2/2);
RightShift = [2:Q,Q];
X1 = permute(X(1:M1,Q+1:M2,:)*ScaleFactor,[2,1,3]);
if rem(M2,2)
X1(Q,1,1) = 0;
end
% Undo lifting stages
X0 = permute(X(1:M1,1:Q,:)/ScaleFactor,[2,1,3]) ...
- filter(LiftFilter(:,4),1,X1,X1(1,:,:)*LiftFilter(1,4),1);
X1 = X1 - filter(LiftFilter(:,3),1,X0(RightShift,:,:),...
X0(1,:,:)*LiftFilter(1,3),1);
X0 = X0 - filter(LiftFilter(:,2),1,X1,...
X1(1,:,:)*LiftFilter(1,2),1);
X1 = X1 - filter(LiftFilter(:,1),1,X0(RightShift,:,:),...
X0(1,:,:)*LiftFilter(1,1),1);
if rem(M2,2)
X1(Q,:,:) = [];
end
X(1:M1,[1:2:M2,2:2:M2],:) = permute([X0;X1],[2,1,3]);
end
%%% Inverse transform along columns %%%
if M1 > 1
Q = ceil(M1/2);
RightShift = [2:Q,Q];
X1 = X(Q+1:M1,1:M2,:)*ScaleFactor;
if rem(M1,2)
X1(Q,1,1) = 0;
end
% Undo lifting stages
X0 = X(1:Q,1:M2,:)/ScaleFactor ...
- filter(LiftFilter(:,4),1,X1,X1(1,:,:)*LiftFilter(1,4),1);
X1 = X1 - filter(LiftFilter(:,3),1,X0(RightShift,:,:),...
X0(1,:,:)*LiftFilter(1,3),1);
X0 = X0 - filter(LiftFilter(:,2),1,X1,...
X1(1,:,:)*LiftFilter(1,2),1);
X1 = X1 - filter(LiftFilter(:,1),1,X0(RightShift,:,:),...
X0(1,:,:)*LiftFilter(1,1),1);
if rem(M1,2)
X1(Q,:,:) = [];
end
X([1:2:M1,2:2:M1],1:M2,:) = [X0;X1];
end
end
end
