t_fastridgexform.m

来自「beamlet变化的工具箱」· M 代码 · 共 84 行

function I = t_FastRidgeXForm(Theta)
% t_FastXRadon: Adjoint Fast Ridgelet transform using the X-interpolator
%  I = t_FastRidgeXForm(Theta)
% Inputs
%	Theta		n*2n transform, in two batches of n columns
% Outputs
%	Image		n*n image, n dyadic
% Description
%	Performs Adjoint of FastRidgeXform
%	Converts between Polar and Cartesian Coordinates
%	in a special X-geometry.  
%   The polar transform associated with continuum
%	data is replaced by a pair of X-s, and the transform
%	is evaluated in that geometry.  To calculate
%	the transform at the polar grid requires re-sampling.

% Programming Notes: 
% Note: use of .' for non-conjugate transpose
% Note: fft_ua requires row vector input

%
%	Diagnostics
%
	nn = size(Theta);
	n = nn(1);
%
%	Boundary-adjusted Inverse Wavelet Transform of Rows
%
	Alpha1 = zeros(n,n);
	Alpha2 = zeros(n,n);
	Theta1 = Theta(:,1:n);
	Theta2 = Theta(:,(n+1):(2*n));
	for j=1:(n),
		Alpha1(j,:) = IWT_CDJV(Theta1(j,:),3,3);
		Alpha2(j,:) = IWT_CDJV(Theta2(j,:),3,3);
	end

%
%	Meyer Wavelet Transform of Columns
%
	X1 = zeros(n,n);
	X2 = zeros(n,n);
	for j=1:(n),
		X1(:,j) = PIWT_YM(Alpha1(:,j).',3,3).';
		X2(:,j) = PIWT_YM(Alpha2(:,j).',3,3).';
	end
%
%	Adjoint Cartesian-to-Polar Conversion
%
	X  = [X1 X2];
	UF = t_Cart_2_RectPolar(X);
%
%	Unbiased Fourier Transform on rows, then columns
%
	I = zeros(n,n);
	for j=1:n,
		f = UF(:,j).';
		g = ifft_ua(f);
		UF(:,j) = g.';
	end
	for i=1:n,
		I(i,:) = ifft_ua(UF(i,:));
	end
	I = real(I);

		
%		
% Copyright (c) 1998 David L. Donoho
%		

%
% Part of BeamLab Version:200
% Built:Friday,23-Aug-2002 00:00:00
% This is Copyrighted Material
% For Copying permissions see COPYING.m
% Comments? e-mail [e-mail]
%
%
% Part of BeamLab Version:200
% Built:Saturday,14-Sep-2002 00:00:00
% This is Copyrighted Material
% For Copying permissions see COPYING.m
% Comments? e-mail [e-mail]
%