def calc_sens(fwd, ex_mat):
"""
see Adler2017 on IEEE TBME, pp 5, figure 6,
Electrical Impedance Tomography: Tissue Properties to Image Measures
"""
# solving EIT problem
p = fwd.solve_eit(ex_mat=ex_mat, parser='fmmu')
v0 = p.v
# normalized jacobian (note: normalize affect sensitivity)
v0 = v0[:, np.newaxis]
jac = p.jac / v0
# calculate sensitivity matrix
s = np.linalg.norm(jac, axis=0)
ae = tri_area(pts, tri)
s = np.sqrt(s) / ae
assert (any(s >= 0))
se = np.log10(s)
sn = sim2pts(pts, tri, se)
return sn
pts = mesh_obj['node']
tri = mesh_obj['element']
# report the status of the 2D mesh
quality.stats(pts, tri)
""" 1. FEM forward simulations """
# setup EIT scan conditions
el_dist, step = 7, 1
ex_mat = eit_scan_lines(16, el_dist)
# calculate simulated data
fwd = Forward(mesh_obj, el_pos)
# in python, index start from 0
ex_line = ex_mat[1].ravel()
# change alpha
anomaly = [{'x': 0.40, 'y': 0.40, 'z': 0.0, 'd': 0.30, 'perm': 100.0}]
mesh_new = mesh.set_perm(mesh_obj, anomaly=anomaly, background=1.0)
tri_perm = mesh_new['perm']
node_perm = sim2pts(pts, tri, np.real(tri_perm))
# solving once using fem
f, _ = fwd.solve(ex_line, perm=tri_perm)
f = np.real(f)
# mplot.tetplot(p, t, edge_color=(0.2, 0.2, 1.0, 1.0), alpha=0.01)
mplot.tetplot(pts, tri, vertex_color=f, alpha=1.0)
# Note: if the jac and the real-problem are generated using the same mesh,
# then, data normalization in solve are not needed.
# However, when you generate jac from a known mesh, but in real-problem
# (mostly) the shape and the electrode positions are not exactly the same
# as in mesh generating the jac, then data must be normalized.
eit = jac.JAC(
mesh_obj,
el_pos,
ex_mat=ex_mat,
step=step,
perm=1.0,
parser="fmmu",
)
eit.setup(p=0.5, lamb=0.01, method="kotre")
ds = eit.solve(f1.v, f0.v, normalize=True)
ds_n = sim2pts(pts, tri, np.real(ds))
# plot ground truth
fig, ax = plt.subplots(figsize=(6, 4))
delta_perm = mesh_new["perm"] - mesh_obj["perm"]
im = ax.tripcolor(x, y, tri, np.real(delta_perm), shading="flat")
fig.colorbar(im)
ax.set_aspect("equal")
# plot EIT reconstruction
fig, ax = plt.subplots(figsize=(6, 4))
im = ax.tripcolor(x, y, tri, ds_n, shading="flat")
for i, e in enumerate(el_pos):
ax.annotate(str(i + 1), xy=(x[e], y[e]), color="r")
fig.colorbar(im)
ax.set_aspect("equal")
"y": 0.5,
"d": 0.2,
"perm": 20
},
{
"x": -0.2,
"y": -0.2,
"d": 0.4,
"perm": 10
},
]
ms1 = wrapper.set_perm(mesh_obj, anomaly=anomaly, background=1.0)
# show delta permittivity on nodes (reverse interp)
ele_ds = ms1["perm"] - ms0["perm"]
node_ds = sim2pts(pts, tri, ele_ds)
# plot
fig, ax = plt.subplots(figsize=(6, 4))
# tripcolor shows values on nodes (shading='flat' or 'gouraud')
im = ax.tripcolor(
pts[:, 0],
pts[:, 1],
tri,
np.real(node_ds),
edgecolor="k",
shading="flat",
alpha=0.8,
cmap=plt.cm.RdBu,
)
# 'tricontour' interpolates values on nodes, for example
""" 1. FEM forward simulations """
# setup EIT scan conditions
el_dist, step = 7, 1
ex_mat = eit_scan_lines(16, el_dist)
# calculate simulated data
fwd = Forward(mesh_obj, el_pos)
# in python, index start from 0
ex_line = ex_mat[2].ravel()
# change alpha
anomaly = [{'x': 0.40, 'y': 0.40, 'z': 0.0, 'd': 0.30, 'perm': 100.0}]
mesh_new = mesh.set_perm(mesh_obj, anomaly=anomaly, background=1.0)
tri_perm = mesh_new['perm']
node_perm = sim2pts(pts, tri, np.real(tri_perm))
# solving once using fem
# f, _ = fwd.solve(ex_line, tri_perm)
# f = np.real(f)
# calculate simulated data
f0 = fwd.solve_eit(ex_mat, step=step, perm=mesh_obj['perm'])
f1 = fwd.solve_eit(ex_mat, step=step, perm=mesh_new['perm'])
""" 3. JAC solver """
# number of stimulation lines/patterns
eit = jac.JAC(mesh_obj,
el_pos,
ex_mat=ex_mat,
step=step,
perm=1.,
f0 = fwd.solve_eit(ex_mat, step=step, perm=mesh_obj['perm'])
f1 = fwd.solve_eit(ex_mat, step=step, perm=mesh_new['perm'])
""" ax2. BP """
eit = bp.BP(mesh_obj, el_pos, ex_mat=ex_mat, step=1, parser='std')
ds = eit.solve(f1.v, f0.v, normalize=True)
ds_bp = ds
""" ax3. JAC """
eit = jac.JAC(mesh_obj, el_pos, ex_mat=ex_mat, step=step,
perm=1., parser='std')
# parameter tuning is needed for better EIT images
eit.setup(p=0.5, lamb=0.1, method='kotre')
# if the jacobian is not normalized, data may not to be normalized too.
ds = eit.solve(f1.v, f0.v, normalize=False)
ds_jac = sim2pts(pts, tri, ds)
""" ax4. GREIT """
eit = greit.GREIT(mesh_obj, el_pos, ex_mat=ex_mat, step=step, parser='std')
# parameter tuning is needed for better EIT images
eit.setup(p=0.5, lamb=0.01)
ds = eit.solve(f1.v, f0.v, normalize=False)
x, y, ds_greit = eit.mask_value(ds, mask_value=np.NAN)
""" build for EIT2016b (orig: 300p x 300p, 150dpi) """
size = (8, 6)
axis_size = [-1.2, 1.2, -1.2, 1.2]
im_size = [-2, 34, -2, 34]
fig = plt.figure(figsize=size)
gs = gridspec.GridSpec(2, 2)
