def calc_cost(x):
cost = 0
for i in range(proj.nsubsets):
# get the slice for the current subset
ss = proj.subset_slices[i]
exp = ppp.pet_fwd_model(x, proj, attn_sino[ss], sens_sino[ss], i, fwhm = fwhm) + contam_sino[ss]
cost += (exp - em_sino[ss]*np.log(exp)).sum()
return cost
sino_params = ppp.PETSinogramParameters(scanner, ntofbins=17, tofbin_width=15.)
proj = ppp.SinogramProjector(scanner,
sino_params,
img.shape,
nsubsets=1,
voxsize=voxsize,
img_origin=img_origin,
ngpus=ngpus,
tof=True,
sigma_tof=60. / 2.35,
n_sigmas=3.)
# estimate the norm of the operator
test_img = np.random.rand(*img.shape)
for i in range(10):
fwd = ppp.pet_fwd_model(test_img, proj, attn_sino, sens_sino, 0, fwhm=fwhm)
back = ppp.pet_back_model(fwd, proj, attn_sino, sens_sino, 0, fwhm=fwhm)
norm = np.linalg.norm(back)
print(i, norm)
test_img = back / norm
# normalize sensitivity sinogram to get PET forward model for 1 view with norm 1
# this is important otherwise the step size T in SPDHG get dominated by the gradient
sens_sino /= (np.sqrt(norm) / proj.sino_params.nviews)
# forward project the image
img_fwd = ppp.pet_fwd_model(img, proj, attn_sino, sens_sino, 0, fwhm=fwhm_data)
# scale sum of fwd image to counts
#---------------------------------------------------------------------------
# generate the sensitivity sinogram
sens_sino = np.ones((nsubsets, sino_shape_nt[0], sino_shape_nt[1] // nsubsets,
sino_shape_nt[2], sino_shape_nt[3]),
dtype=np.float32) / pr_norm
img_fwd = np.zeros((nsubsets, sino_shape[0], sino_shape[1] // nsubsets,
sino_shape[2], sino_shape[3]),
dtype=np.float32)
# forward project the image
for i in range(nsubsets):
img_fwd[i, ...] = ppp.pet_fwd_model(img,
proj,
attn_sino,
sens_sino,
i,
fwhm=fwhm_data)
# scale sum of fwd image to counts
if counts > 0:
scale_fac = (counts / img_fwd.sum())
img_fwd *= scale_fac
img *= scale_fac
# contamination sinogram with scatter and randoms
contam_sino = np.full(img_fwd.shape,
0.2 * img_fwd.mean(),
dtype=np.float32)
em_sino = np.random.poisson(img_fwd + contam_sino)