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EIDORS: Electrical Impedance Tomography and Diffuse Optical Tomography Reconstruction Software |
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Banana-shaped minima region in objective functionOne of the challenges of inverse problems is that the line search often must go through minima regions that have challenging shapes. This tutorial illustrates a "banana"-shaped minimum region
imb= mk_common_model('a2c2',16);
img= mk_image(imb,1); %show_fem(img,[0,0,1]);
vv = fwd_solve(img); vv = vv.meas;
p1 = [29,28]; p2 = [19,20];
sp = logspace(-2.5,2.5,40);
for i = length(sp):-1:1
for j = length(sp):-1:1
img.elem_data(p1) = sp(i);
img.elem_data(p2) = sp(j);
v2 = fwd_solve(img);
M(i,j) = norm(vv-v2.meas);
end
end
img.elem_data(p1) = 10^(+.1);
img.elem_data(p2) = 10^(-.1);
subplot(121);show_fem(img,[0,0,1]);
clim = [min(M(:)),max(M(:))]*(eye(2)-[1,0;1,0]/20);
subplot(122);imagesc(log10(sp),log10(sp),M,clim); axis image
print_convert minima_region_01a.jpg
Figure: Left: forward model with two regions (blue and red). Right: objective function as a function of the conductivity in each region |
Last Modified: $Date: 2017-02-28 13:12:08 -0500 (Tue, 28 Feb 2017) $ by $Author: aadler $