ifrt_rp.m

来自「beamlet变化的工具箱」· M 代码 · 共 91 行

function I = IFRT_RP(Theta,Anomaly)
% IFRT_RP: Adjoint Fast Ridgelet transform using RectoPolar
%  I = IFRT_RP(Theta,Anomaly)
% Inputs
%	Theta		n*2n transform, in two batches of n columns
%	Anomaly		2*n	 extra piece of transform
% Outputs
%	Image		n*n image, n dyadic
% Description
%	Performs Inverse of FRT_RP
%	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));
	bump = 16;
	levl = 3;
	for j=1:(n),
		Alpha1(j,:) = IWT_CDJV(Theta1(j,:),levl,3);
		Alpha2(j,:) = IWT_CDJV(Theta2(j,:),levl,3);
		if j==bump,
			levl = levl+1;
			bump = 2*bump;
		end
	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
%
%	Inverse Cartesian-to-Polar Conversion
%
	X = [X1 X2];
	X(1,:) = X(1,:) + sqrt(-1).*Anomaly;
	UF = RectPolr2Cart_CG(X,1,10,.001,0);
%
%	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) 1998,1999,2000 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]
%