EIDORS: Electrical Impedance Tomography and Diffuse Optical Tomography Reconstruction Software

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Dual Models − Coarse model partially covers fine model

Coarse and Fine models

% Dual Partial $Id: dual_partial2d01.m 1535 2008-07-26 15:36:27Z aadler $

imdl= mk_common_model('d2c2',64);
fmdl= imdl.fwd_model;
% Only keep 11 electrodes on top
fmdl.electrode = fmdl.electrode([60:64,1:6]);
% New stimulation pattern with 11 electrodes
fmdl.stimulation = mk_stim_patterns(11,1,'{ad}','{ad}',{},1);
% Remove meas_select - it was created for 64 electrodes
fmdl = rmfield(fmdl,'meas_select'); 
subplot(121)
show_fem(fmdl); axis square

% Crop model
[cmdl,c2f_idx]= crop_model(fmdl, inline('(y-0.25)-abs(x)>0','x','y','z'));
subplot(122)
show_fem(cmdl);
axis(1.05*[-1 1 -1 1]); axis square;

print -r125 -dpng dual_partial2d01a.png;

Figure: Fine (left) and dual (right) models

Simulated data

% Simulate object moving $Id: dual_partial2d02.m 1535 2008-07-26 15:36:27Z aadler $

% simulation model
imdl= mk_common_model('d2c2',64);
smdl= imdl.fwd_model;
% Only keep 11 electrodes on top 
smdl.electrode = smdl.electrode([60:64,1:6]);
smdl.stimulation = mk_stim_patterns(11,1,'{ad}','{ad}',{},1);

[vh,vi,xyr]= simulate_2d_movement(32, smdl, [0.75,0.05] );
% Only 12 to 2 O'clock
idx= 25:30;
vi= vi(:,idx); xyr= xyr(:,idx);

clf;subplot(121)
show_fem(smdl); axis square

% Show target positions
   theta= linspace(0,2*pi,50); xr= cos(theta); yr= sin(theta);
   hold on;
   for i=1:size(xyr,2)
       hh= plot(xyr(3,i)*xr+ xyr(1,i),xyr(3,i)*yr+ xyr(2,i));
       set(hh,'LineWidth',3,'Color',[0,0,0]);
   end
   hold off;



print -r125 -dpng dual_partial2d02a.png;

Figure: Simulation data

Reconstruction models

% Dual Partial $Id: dual_partial2d03.m 1535 2008-07-26 15:36:27Z aadler $

% base model
imdl.RtR_prior = @noser_image_prior;
imdl.hyperparameter.value = 3e-2;

% Reconstruction model - only fine reconstruction
frec_mdl= imdl;
frec_mdl.fwd_model= fmdl; % fine model

% Reconstruction model - dual model
drec_mdl = imdl;
drec_mdl.fwd_model= fmdl; % fine model
% coarse to fine mapping
nf_els= size(fmdl.elems,1); nc_els= size(cmdl.elems,1);
drec_mdl.fwd_model.coarse2fine= sparse(c2f_idx, 1:nc_els, 1, nf_els, nc_els);

Reconstructed images (projected to fine mesh)

% Dual Partial $Id: dual_partial2d04.m 1535 2008-07-26 15:36:27Z aadler $

clf; levels= [inf,inf,0,1,1];

% reconstruct fine model
imgf= inv_solve(frec_mdl, vh, vi);

show_slices(imgf,levels);
print -r125 -dpng dual_partial2d04a.png;

% reconstruct dual model
imgd= inv_solve(drec_mdl, vh, vi);

show_slices(imgd,levels);
print -r125 -dpng dual_partial2d04b.png;

Figure: Fine (top) and dual (bottom) reconstructed images

Reconstructed images (projected to coarse mesh)

% Dual Partial $Id: dual_partial2d05.m 1535 2008-07-26 15:36:27Z aadler $

clf; levels= [inf,inf,0,1,1];

% reconstruct fine model params onto coarse model
imgf= inv_solve(frec_mdl, vh, vi);
imgf.fwd_model= cmdl;
imgf.elem_data= imgf.elem_data(c2f_idx,:);

show_slices(imgf,levels);
print -r125 -dpng dual_partial2d05a.png;

% reconstruct dual model on coarse mesh
imgd= inv_solve(drec_mdl, vh, vi);
imgd.fwd_model= cmdl;

show_slices(imgd,levels);
print -r125 -dpng dual_partial2d05b.png;

Figure: Fine (top) and dual (bottom) reconstructed images