plt.semilogy(criter_CGLS)
plt.title('CGLS criterion')
plt.show()
# CGLS solves the simple least-squares problem. The same problem can be solved
# by FISTA by setting up explicitly a least squares function object and using
# no regularisation:
# Create least squares object instance with projector, test data and a constant
# coefficient of 0.5:
f = Norm2sq(Cop, b, c=0.5)
# Run FISTA for least squares without regularization
x_fista0, it0, timing0, criter0 = FISTA(x_init, f, None, opt=opt)
plt.imshow(x_fista0.subset(vertical=0).array)
plt.title('FISTA Least squares')
plt.show()
plt.semilogy(criter0)
plt.title('FISTA Least squares criterion')
plt.show()
# FISTA can also solve regularised forms by specifying a second function object
# such as 1-norm regularisation with choice of regularisation parameter lam:
# Create 1-norm function object
lam = 0.1
g0 = Norm1(lam)
# Run FISTA for least squares plus 1-norm function.
plt.show()
# Set initial guess
print("Initial guess")
x_init = ImageData(geometry=ig)
# Create least squares object instance with projector and data.
print("Create least squares object instance with projector and data.")
f = Norm2sq(Cop, padded_data2, c=0.5)
# Run FISTA reconstruction for least squares without regularization
print("Run FISTA for least squares")
opt = {'tol': 1e-4, 'iter': 100}
x_fista0, it0, timing0, criter0 = FISTA(x_init, f, None, opt=opt)
plt.imshow(x_fista0.subset(horizontal_x=80).array)
plt.title('FISTA LS')
plt.colorbar()
plt.show()
# Set up 1-norm function for FISTA least squares plus 1-norm regularisation
print("Run FISTA for least squares plus 1-norm regularisation")
lam = 0.1
g0 = Norm1(lam)
# Run FISTA for least squares plus 1-norm function.
x_fista1, it1, timing1, criter1 = FISTA(x_init, f, g0, opt=opt)
plt.imshow(x_fista0.subset(horizontal_x=80).array)
plt.title('FISTA LS+1')
plt.colorbar()
plt.semilogy(criter_CGLS)
plt.title('CGLS Criterion vs iterations')
plt.show()
# Create least squares object instance with projector, test data and a constant
# coefficient of 0.5. Note it is least squares over all channels.
f = Norm2sq(Aall, data2d, c=0.5)
# Options for FISTA algorithm.
opt = {'tol': 1e-4, 'iter': 100}
# Run FISTA for least squares without regularization and display one channel
# reconstruction as image.
x_fista0, it0, timing0, criter0 = FISTA(x_init, f, None, opt)
plt.imshow(x_fista0.subset(channel=100).array)
plt.title('FISTA LS')
plt.show()
plt.semilogy(criter0)
plt.title('FISTA LS Criterion vs iterations')
plt.show()
# Set up 1-norm regularisation (over all channels), solve with FISTA, and
# display one channel of reconstruction.
lam = 0.1
g0 = Norm1(lam)
x_fista1, it1, timing1, criter1 = FISTA(x_init, f, g0, opt)
plt.imshow(x_fista1.subset(channel=100).array)