EIDORS: Electrical Impedance Tomography and Diffuse Optical Tomography Reconstruction Software 
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GREIT algorithm: Sheffield backprojectionThere are several different versions of the backprojection algorithm in existence. The one made available here is the version distributed with the Sheffield Mk I system, and is very similar to the algorithm distributed with the Göttingen Goe MF II EIT system. Almost all clinical and experimental publications which mention "backprojection" use the version of the algorithm provided here. The paper which probably best describes this algorithm is Santosa, F. and Vogelius, M. (1990) Backprojection algorithm for electrical impedance imaging, SIAM J. Applied Mathematics, 50:216−243.This matrix is copyright DC Barber and BH Brown at University of Sheffield. It may be used free of charge for research and noncommercial purposes. Commercial applications require a licence from the University of Sheffield. GREIT Sheffield Backprojection reconstruction functionThis code requires the backprojection matrix from herefunction [img,map]= GREIT_Sheffield_backproj( ref_meas, reconst_meas ) [RM,map] = calc_backproj_matrix; % Expand ref_meas to the full size of reconst_meas num_meas = size(reconst_meas,2); ref_meas = ref_meas * ones(1,num_meas); dv = ( reconst_meas  ref_meas ) ./ ref_meas; % CHANGE IS HERE: % reconst image ds = RM*dv; img= reshape(ds, 32,32,num_meas); function [RM,map] = calc_backproj_matrix; [x,y]= meshgrid(1:16,1:16); % Take a slice ss1 = (yx)>1 & (yx)<15; sel1 = abs(xy)>1 & abs(xy)<15; [x,y]= meshgrid(15.5:15.5,15.5:15.5); ss2 = abs(xy)<25 & abs(x+y)<25 & x<0 & y<0 & x>=y ; sel2 = abs(xy)<25 & abs(x+y)<25; load Sheffield_Backproj_Matrix.mat BP = zeros(16^2, 32^2); BP(ss1,ss2) = Sheffield_Backproj_Matrix; BP = reshape(BP, 16,16,32,32); % Build up BP = BP + permute(BP, [2,1,3,4]); % Reciprocity % FLIP LR el= 16:1:1; BP= BP + BP(el,el,[32:1:1],:); % FLIP UD el= [8:1:1,16:1:9]; BP= BP + BP(el,el,:,[32:1:1]); % Transpose el= [12:1:1,16:1:13]; BP= BP + permute(BP(el,el,:,:), [1,2,4,3]); % Final flip to match radiological view (upward toward patient) BP = permute(BP, [1,2,4,3]); RM= reshape(BP, 256, [])'; RM= RM(:,sel1); map = sel2; 
Last Modified: $Date: 20170228 13:12:08 0500 (Tue, 28 Feb 2017) $ by $Author: aadler $