changeset 50:d5155eaa3f68

(none)

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Problems/private/genPDF.m	Mon Mar 14 16:51:46 2011 +0000
@@ -0,0 +1,113 @@
+function [pdf,val] = genPDF(imSize,p,pctg,distType,radius,disp)
+
+%[pdf,val] = genPDF(imSize,p,pctg [,distType,radius,disp])
+%
+%	generates a pdf for a 1d or 2d random sampling pattern
+%	with polynomial variable density sampling
+%
+%	Input:
+%		imSize - size of matrix or vector
+%		p - power of polynomial
+%		pctg - partial sampling factor e.g. 0.5 for half
+%		distType - 1 or 2 for L1 or L2 distance measure
+%		radius - radius of fully sampled center
+%		disp - display output
+%
+%	Output:
+%		pdf - the pdf
+%		val - min sampling density
+%
+% 
+%	Example:
+%	[pdf,val] = genPDF([128,128],2,0.5,2,0,1);
+%
+%	(c) Michael Lustig 2007
+
+%   This file is used with the kind permission of Michael Lustig
+%   ([e-mail]), and originally appeared in the
+%   SparseMRI toolbox, http://www.stanford.edu/~mlustig/ .
+%
+% $Id: genPDF.m 1040 2008-06-26 20:29:02Z ewout78 $
+
+
+if nargin < 4
+	distType = 2;
+end
+
+if nargin < 5
+	radius = 0;
+end
+
+if nargin < 6
+	disp = 0;
+end
+
+
+minval=0;
+maxval=1;
+val = 0.5;
+
+if length(imSize)==1
+	imSize = [imSize,1];
+end
+
+sx = imSize(1);
+sy = imSize(2);
+PCTG = floor(pctg*sx*sy);
+
+
+if sum(imSize==1)==0  % 2D
+	[x,y] = meshgrid(linspace(-1,1,sy),linspace(-1,1,sx));
+	switch distType
+		case 1
+			r = max(abs(x),abs(y));
+		otherwise
+			r = sqrt(x.^2+y.^2);
+			r = r/max(abs(r(:)));			
+	end
+
+else %1d
+	r = abs(linspace(-1,1,max(sx,sy)));
+end
+
+
+
+
+idx = find(r<radius);
+
+pdf = (1-r).^p; pdf(idx) = 1;
+if floor(sum(pdf(:))) > PCTG
+	error('infeasible without undersampling dc, increase p');
+end
+
+% begin bisection
+while(1)
+	val = minval/2 + maxval/2;
+	pdf = (1-r).^p + val; pdf(find(pdf>1)) = 1; pdf(idx)=1;
+	N = floor(sum(pdf(:)));
+	if N > PCTG % infeasible
+		maxval=val;
+	end
+	if N < PCTG % feasible, but not optimal
+		minval=val;
+	end
+	if N==PCTG % optimal
+		break;
+	end
+end
+
+if disp
+	figure, 
+	subplot(211), imshow(pdf)
+	if sum(imSize==1)==0
+		subplot(212), plot(pdf(end/2+1,:));
+	else
+		subplot(212), plot(pdf);
+	end
+end
+
+
+
+
+
+