EIDORS: Electrical Impedance Tomography and Diffuse Optical Tomography Reconstruction Software

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Reconstructing with electrode errors

Sample Data and clean reconstruction

% Sample data + Image $Id: electrode_errors01.m 2392 2010-11-14 09:07:49Z aadler $

% Sample data
load montreal_data_1995
vi = double( zc_resp );
vh = double( zc_resp(:,1) );

% Reconstruct
imdl = mk_common_model('c2t2',16);
imdl.hyperparameter.value = .1;

img = inv_solve(imdl, vh, vi);
subplot(221)
show_slices(img);
print_convert electrode_errors01a.jpg

img = inv_solve(imdl, vh, vi(:,20));
show_fem(img,[0,1,0]);
print_convert electrode_errors01b.jpg

Figure: Reconstructions of breathing data, illustrating that a small amount of electrode error occurs at electrodes 13 and 5.

Eliminating Electrodes

Andy Adler Reference Accounting for erroneous electrode data in EIT Physiol Meas, 25(1):227-238, 2004.

% Reject electrodes + Image $Id: electrode_errors02.m 2391 2010-11-13 10:53:29Z aadler $


imdl.meas_icov = meas_icov_rm_elecs( imdl, 13);

img = inv_solve(imdl, vh, vi(:,20));
show_fem(img,[0,1,0]);
print_convert electrode_errors02a.jpg

imdl.meas_icov = meas_icov_rm_elecs( imdl, [13,5]);

img = inv_solve(imdl, vh, vi(:,20));
show_fem(img,[0,1,0]);
print_convert electrode_errors02b.jpg

Figure: Reconstructions removing Left: Electrode 13, and Right: Electrodes 5 and 13

Detecting and automatically eliminating electrodes

AE Hartinger, R Guardo, A Adler, H Gagnon. Real-time management of faulty electrodes in EIT IEEE T BME 2008.

% Reciprocity error + Image $Id: electrode_errors03.m 2392 2010-11-14 09:07:49Z aadler $

imdl.calc_reciproc_error.tau = 3e-4;
imdl.meas_icov = calc_reciproc_error( imdl, vi );

img = inv_solve(imdl, vh, vi(:,20)); show_fem(img,[0,1,0]);
print_convert electrode_errors03a.jpg

imdl.calc_reciproc_error.tau = 3e-2;
imdl.meas_icov = calc_reciproc_error( imdl, vi );

img = inv_solve(imdl, vh, vi(:,20)); show_fem(img,[0,1,0]);
print_convert electrode_errors03b.jpg

Figure: Reconstructions removing Left: Parameter τ=0.0003 Right: Parameter τ=0.03

Electrode Errors with GREIT

Create a GREIT model.

% Reject electrodes + Image $Id: electrode_errors04.m 2878 2012-02-20 10:13:20Z aadler $

fmdl= mk_library_model('adult_male_16el_lungs');
fmdl.electrode = fmdl.electrode([9:16,1:8]);

[stim,msel] = mk_stim_patterns(16,1,[0,1],[0,1],{'no_meas_current'},1);
fmdl.stimulation = stim;
fmdl.normalize_measurements=1;
fmdl.meas_select = msel;
img = mk_image(fmdl, 1);
img.elem_data([fmdl.mat_idx{2};fmdl.mat_idx{3}]) = 0.3; % lungs
clear opt; opt.imgsz = [32 32]; opt.square_pixels=1;
opt.noise_figure = .5;
imdl=mk_GREIT_model(img, 0.25, [], opt);

% Basic GREIT reconst $Id: electrode_errors05.m 2875 2012-02-20 07:51:20Z aadler $

imgr= inv_solve(imdl, zc_resp(:,1), zc_resp(:,22));
imgr.calc_colours.ref_level=0; show_fem(imgr,[0,1]);

axis equal; axis([-1,1.05,-.8,.8]);
print_convert electrode_errors05a.jpg

Figure: Basic GREIT reconstruction

% GREIT - error $Id: electrode_errors06.m 2878 2012-02-20 10:13:20Z aadler $

imdl = eidors_obj('inv_model','','fwd_model',fmdl);
imdl.meas_icov_rm_elecs.elec_list = 13;
imdl.meas_icov_rm_elecs.exponent  = -1;
imdl.meas_icov_rm_elecs.SNR       = 100;
opt.noise_covar = meas_icov_rm_elecs(imdl);
imdl=mk_GREIT_model(img, 0.25, [], opt);

imgr= inv_solve(imdl, zc_resp(:,1), zc_resp(:,22));
imgr.calc_colours.ref_level=0; show_fem(imgr,[0,1]);

axis equal; axis([-1,1.05,-.8,.8]);
print_convert electrode_errors06a.jpg

Figure: Basic GREIT reconstruction

% Basic GREIT reconst $Id: electrode_errors07.m 2878 2012-02-20 10:13:20Z aadler $

% use -ve tau to get covariance rather than inv covar
imdl.calc_reciproc_error.tau = -3e-4;
opt.noise_covar = calc_reciproc_error( imdl, zc_resp );

imdl=mk_GREIT_model(img, 0.25, [], opt);

imgr= inv_solve(imdl, zc_resp(:,1), zc_resp(:,22));
imgr.calc_colours.ref_level=0; show_fem(imgr,[0,1]);

axis equal; axis([-1,1.05,-.8,.8]);

print_convert electrode_errors07a.jpg

Figure: Basic GREIT reconstruction