Contributed EIT Data:

Authors: David C Barber, Brian H Brown
Date: June 2008
Brief Description: There 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.
License: This matrix is copyright DC Barber and BH Brown at University of Sheffield. It may be used free of charge for research and non-commercial purposes. Commercial applications require a licence from the University of Sheffield.
Attribution Requirement: Publications or presentations using these data should reference this publication: D.C. Barber and B.H. Brown (1984), Applied Potential Tomography, J. Phys. E: Sci. Instrum., 17:723-733.
Format: In order to save space, only 1/8 of the image and 1/2 (reciprocity values) of the measurements are stored. In order to unpackage it, the following code from mk_common_gridmdl may be used:
   [x,y]= meshgrid(1:16,1:16); % Take a slice
   ss1 = (y-x)>1 & (y-x)<15;
   sel1 = abs(x-y)>1 & abs(x-y)<15;
   [x,y]= meshgrid(-15.5:15.5,-15.5:15.5);
   ss2 = abs(x-y)<25 & abs(x+y)<25 & x<0 & y<0 & x>=y ;
   sel2 = abs(x-y)<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
   el= 16:-1:1;           BP= BP + BP(el,el,[32:-1:1],:); % FLIP LR
   el= [8:-1:1,16:-1:9];  BP= BP + BP(el,el,:,[32:-1:1]); % FLIP UD
   el= [12:-1:1,16:-1:13]; BP= BP + permute(BP(el,el,:,:), [1,2,4,3]); % Transpose
   RM= reshape(BP, 256, [])'; RM= RM(sel2,sel1);

Data: The Backprojection matrix is distributed with EIDORS (version≥3.3) in the sample_data directory.


A simple example compares GN reconstruction to that of backprojection, showing the 32×32 grid on which it is reconstructed Last Modified: $Date: 2017-02-28 13:12:08 -0500 (Tue, 28 Feb 2017) $ by $Author: aadler $