# W_x = NufftObj.xx2k( NufftObj.adjoint(NufftObj.forward(NufftObj.k2xx(W0))))
# W_y = NufftObj.xx2k(NufftObj.x2xx(NufftObj.adjoint(NufftObj.k2y(W0))))
W = NufftObj.xx2k(NufftObj.adjoint(W0))
# W = NufftObj.y2k(W0)
# matplotlib.pyplot.subplot(1,)
matplotlib.pyplot.imshow(numpy.real((W * W.conj())**0.5))
matplotlib.pyplot.title('Ueckers inverse function (real)')
# matplotlib.pyplot.subplot(1,2,2)
# matplotlib.pyplot.imshow(W.imag)
# matplotlib.pyplot.title('Ueckers inverse function (imaginary)')
matplotlib.pyplot.show()
p0 = NufftObj.adjoint(NufftObj.forward(image))
p1 = NufftObj.k2xx((W.conj() * W)**0.5 * NufftObj.xx2k(image))
print('error between Toeplitz and Inverse reconstruction',
numpy.linalg.norm(p1 - p0) / numpy.linalg.norm(p0))
matplotlib.pyplot.subplot(1, 3, 1)
matplotlib.pyplot.imshow(numpy.real(p0))
matplotlib.pyplot.title('Toeplitz')
matplotlib.pyplot.subplot(1, 3, 2)
matplotlib.pyplot.imshow(numpy.real(p1))
matplotlib.pyplot.title('Ueckers inverse function')
matplotlib.pyplot.subplot(1, 3, 3)
matplotlib.pyplot.imshow(numpy.abs(p0 - p1) / numpy.abs(p1))
matplotlib.pyplot.title('Difference')
matplotlib.pyplot.show()
def test_2D():
import pkg_resources
DATA_PATH = pkg_resources.resource_filename('pynufft', 'src/data/')
# PHANTOM_FILE = pkg_resources.resource_filename('pynufft', 'data/phantom_256_256.txt')
import numpy
import matplotlib.pyplot
from pynufft import NUFFT_cpu
# load example image
# image = numpy.loadtxt(DATA_PATH +'phantom_256_256.txt')
image = scipy.misc.ascent()
image = scipy.misc.imresize(image, (256, 256))
image = image.astype(numpy.float) / numpy.max(image[...])
#numpy.save('phantom_256_256',image)
matplotlib.pyplot.imshow(image, cmap=matplotlib.cm.gray)
matplotlib.pyplot.show()
print('loading image...')
Nd = (256, 256) # image size
print('setting image dimension Nd...', Nd)
Kd = (512, 512) # k-space size
print('setting spectrum dimension Kd...', Kd)
Jd = (6, 6) # interpolation size
print('setting interpolation size Jd...', Jd)
# load k-space points
# om = numpy.loadtxt(DATA_PATH+'om.txt')
om = numpy.load(DATA_PATH + 'om2D.npz')['arr_0']
print('setting non-uniform coordinates...')
matplotlib.pyplot.plot(om[::10, 0], om[::10, 1], 'o')
matplotlib.pyplot.title('non-uniform coordinates')
matplotlib.pyplot.xlabel('axis 0')
matplotlib.pyplot.ylabel('axis 1')
matplotlib.pyplot.show()
NufftObj = NUFFT_cpu()
NufftObj.plan(om, Nd, Kd, Jd)
y = NufftObj.forward(image)
print('setting non-uniform data')
print('y is an (M,) list', type(y), y.shape)
W = numpy.ones(Kd, dtype=numpy.complex64)
for pp in range(0, 200):
W2 = NufftObj.xx2k(NufftObj.adjoint(NufftObj.forward(
NufftObj.k2xx(W))))
W2 = W2 * W2.conj()
W2 = W2**0.5
W = (W + 0.9) / (W2 + 0.9)
matplotlib.pyplot.subplot(1, 2, 1)
matplotlib.pyplot.imshow(W2.real)
matplotlib.pyplot.subplot(1, 2, 2)
matplotlib.pyplot.imshow((W / W2).real)
matplotlib.pyplot.show()
# kspectrum = NufftObj.xx2k( NufftObj.solve(y,solver='bicgstab',maxiter = 100))
image_restore = NufftObj.solve(y, solver='cg', maxiter=10)
shifted_kspectrum = numpy.fft.fftshift(
numpy.fft.fftn(numpy.fft.fftshift(image_restore)))
print('getting the k-space spectrum, shape =', shifted_kspectrum.shape)
print('Showing the shifted k-space spectrum')
matplotlib.pyplot.imshow(shifted_kspectrum.real,
cmap=matplotlib.cm.gray,
norm=matplotlib.colors.Normalize(vmin=-100,
vmax=100))
matplotlib.pyplot.title('shifted k-space spectrum')
matplotlib.pyplot.show()
image2 = NufftObj.solve(y, 'dc', maxiter=25)
# image3 = NufftObj.solve(y, 'L1TVLAD',maxiter=100, rho= 1)
image3 = NufftObj.k2xx(NufftObj.xx2k(NufftObj.adjoint(y)) * W)
print(image3.shape)
image4 = NufftObj.solve(y, 'L1TVOLS', maxiter=100, rho=1)
matplotlib.pyplot.subplot(1, 3, 1)
matplotlib.pyplot.imshow(image,
cmap=matplotlib.cm.gray,
norm=matplotlib.colors.Normalize(vmin=0.0,
vmax=1))
matplotlib.pyplot.subplot(1, 3, 2)
matplotlib.pyplot.imshow(image3.real,
cmap=matplotlib.cm.gray,
norm=matplotlib.colors.Normalize(vmin=0.0,
vmax=1))
matplotlib.pyplot.subplot(1, 3, 3)
matplotlib.pyplot.imshow(image4.real,
cmap=matplotlib.cm.gray,
norm=matplotlib.colors.Normalize(vmin=0.0,
vmax=1))
matplotlib.pyplot.show()
# matplotlib.pyplot.imshow(image2.real, cmap=matplotlib.cm.gray, norm=matplotlib.colors.Normalize(vmin=0.0, vmax=1))
# matplotlib.pyplot.show()
maxiter = 25
counter = 1
for solver in ('dc', 'bicg', 'bicgstab', 'cg', 'gmres', 'lgmres', 'lsmr',
'lsqr'):
print(counter, solver)
if 'lsqr' == solver:
image2 = NufftObj.solve(y, solver, iter_lim=maxiter)
else:
image2 = NufftObj.solve(y, solver, maxiter=maxiter)
# image2 = NufftObj.solve(y, solver='bicgstab',maxiter=30)
matplotlib.pyplot.subplot(2, 4, counter)
matplotlib.pyplot.imshow(image2.real,
cmap=matplotlib.cm.gray,
norm=matplotlib.colors.Normalize(vmin=0.0,
vmax=1))
matplotlib.pyplot.title(solver)
# print(counter, solver)
counter += 1
matplotlib.pyplot.show()