nufft_r.m

著名的Sparco工具包。是matlab下解决线性约束

 function [rr, arg] = nufft_r(om, N, J, K, alpha, beta, use_true_diric)
%function [rr, arg] = nufft_r(om, N, J, K, alpha, beta, use_true_diric)
% make NUFFT "r" vector
% in:
%	om	[M,1]	digital frequency omega in radians
%	N		signal length
%	J		# of neighbors used per frequency location
%	K		FFT size (should be > N)
%	alpha	[0:L]	Fourier series coefficients of scaling factors
%	beta		scale gamma=2pi/K by this in Fourier series
%				typically is K/N (me) or 0.5 (Liu)
% out:
%	rr	[J,M]	r vector for each frequency
%	arg	[J,M]	dirac argument for t=0
%
% Copyright 2001-12-13, Jeff Fessler, The University of Michigan

if nargin < 4, help(mfilename), error(mfilename), end
if ~isvar('alpha') | isempty(alpha)
	alpha = [1];	% default Fourier series coefficients of scaling factors
end
if ~isvar('beta') | isempty(beta)
	beta = 0.5;	% default is Liu version for now
end
if ~isvar('use_true_diric') | isempty(use_true_diric)
	use_true_diric = false;
end

M = length(om);
gam = 2*pi/K;
dk = om / gam - nufft_offset(om, J, K);		% [M,1]
arg = outer_sum(-[1:J]', dk');			% [J,M] diric arg for t=0

L = length(alpha) - 1;
if ~isreal(alpha(1)), error 'need real alpha_0', end

if L > 0
	rr = zeros(J,M);
	for l1 = -L:L
		alf = alpha(abs(l1)+1);
		if l1<0, alf = conj(alf); end
		r1 = nufft_diric(arg + l1 * beta, N, K, use_true_diric);
		rr = rr + alf * r1;			% [J,M]
	end
else
	rr = nufft_diric(arg, N, K, use_true_diric);	% [J,M]
end