script_3D.py
special_license='''
The license of the 3D Shepp-Logan phantom:
Copyright (c) 2006, Matthias Schabel
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are
met:
* Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in
the documentation and/or other materials provided with the distribution
* Neither the name of the University of Utah Department of Radiology nor the names
of its contributors may be used to endorse or promote products derived
from this software without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
POSSIBILITY OF SUCH DAMAGE.
'''
import numpy
import matplotlib.pyplot as pyplot
from matplotlib import cm
gray = cm.gray
def indxmap_diff(Nd):
"""
Preindixing for rapid image gradient ()
Diff(x) = x.flat[d_indx[0]] - x.flat
Diff_t(x) = x.flat[dt_indx[0]] - x.flat
:param Nd: the dimension of the image
:type Nd: tuple with integers
:returns d_indx: image gradient
:returns dt_indx: the transpose of the image gradient
:rtype: d_indx: lists with numpy ndarray
:rtype: dt_indx: lists with numpy ndarray
"""
ndims = len(Nd)
Ndprod = numpy.prod(Nd)
mylist = numpy.arange(0, Ndprod).astype(numpy.int32)
mylist = numpy.reshape(mylist, Nd)
d_indx = []
dt_indx = []
for pp in range(0, ndims):
d_indx = d_indx + [ numpy.reshape( numpy.roll( mylist, +1 , pp ), (Ndprod,) ,order='C').astype(numpy.int32) ,]
dt_indx = dt_indx + [ numpy.reshape( numpy.roll( mylist, -1 , pp ) , (Ndprod,) ,order='C').astype(numpy.int32) ,]
return d_indx, dt_indx
import scipy.sparse
def gradient_class(Nd, axis):
d_indx, dt_indx = indxmap_diff(Nd)
I = scipy.sparse.eye(numpy.prod(Nd), numpy.prod(Nd))
data = numpy.ones((numpy.prod(Nd),))
row_ind = d_indx[axis]
col_ind= numpy.arange(0, numpy.prod(Nd)).astype(numpy.int)
G = scipy.sparse.csr_matrix(( data,
(row_ind, col_ind)), shape = (numpy.prod(Nd),numpy.prod(Nd))
)
G = G- I
G = G.tocsr()
return G
def gradient_class2(Nd, axis):
d_indx, dt_indx = indxmap_diff(Nd)
I = scipy.sparse.eye(numpy.prod(Nd), numpy.prod(Nd))
data = numpy.ones((numpy.prod(Nd),))
row_ind = dt_indx[axis]
col_ind= numpy.arange(0, numpy.prod(Nd)).astype(numpy.int)
G = scipy.sparse.csr_matrix(( data,
(row_ind, col_ind)), shape = (numpy.prod(Nd),numpy.prod(Nd))
)
G = G- I
G = G.tocsr()
return G
def GBPDNA_old(nufft, gy, maxiter):
"""
GBPDNA: test 3D total variation
"""
import pynufft.src._helper.helper as helper
f = gy.get()
def A(x):
px = numpy.array(x.astype(numpy.complex64), order='C')
y2 = nufft.forward(nufft.thr.to_device(numpy.reshape(px, nufft.st['Nd']))).get()
return y2
def AH(y):
py = numpy.array(y.astype(numpy.complex64), order='C')
x2 = nufft.adjoint(nufft.thr.to_device(py)).get().flatten()
return x2
Nd = nufft.st['Nd']
Gx = gradient_class(Nd, 0)
Gy = gradient_class(Nd, 1)
Gz = gradient_class(Nd, 2)
Gx2 = gradient_class2(Nd, 0)
Gy2 = gradient_class2(Nd, 1)
Gz2 = gradient_class2(Nd, 2)
M = nufft.st['M']
v = numpy.ones(M,)
for pp in range(0,20):
w = A(AH((v)))
lab = numpy.inner(w,numpy.conj(v))/numpy.inner(v,numpy.conj(v))
tau_1 = 1/lab.real
# print(lab, tau_1)
w = w/numpy.linalg.norm(w)
v= w
v= numpy.random.rand(numpy.prod(Nd),)
for pp in range(0,20):
w = Gx.getH().dot(Gx.dot(v))
lab = numpy.inner(w,numpy.conj(v))/numpy.inner(v,numpy.conj(v))
tau_2 = 1/(lab.real)
w = w/numpy.linalg.norm(w)
v= w
print("tau_1 = ", tau_1)
print("tau_2 = ", tau_2)
# tau_1 = 0.1*tau_1
tau_2 = 0.01*tau_2
# tau_2 *= 3
delta = 1.0
mu = 0.001*numpy.max(numpy.abs(AH(f))[...])
print("mu=",mu)
def P_lambda(w_i, mu, tau_1):
w_abs = numpy.abs(w_i)
# print(w_abs.shape)
# print(w_iw_abs.shape)
out = ((w_i+1e-10)/(w_abs+1e-10))*mu/tau_1
indx= w_abs <= (mu/tau_1)
out[indx] =w_i[indx]
return out
def Q_f_eps(v, f, eps):
v_f = v-f
v_f_abs = numpy.abs(v_f)
out = f + eps* v_f/v_f_abs
indx = (v_f_abs <= eps)
out[indx] = v[indx]
return out
N = numpy.prod(Nd)
u_bold_k = numpy.zeros(N,)
v_k = numpy.zeros(M,)
z_k = numpy.zeros(M,)
w_kx = numpy.zeros(N,)
w_ky = numpy.zeros(N,)
w_kz = numpy.zeros(N,)
# w_kx2 = numpy.zeros(N,)
# w_ky2 = numpy.zeros(N,)
# w_kz2 = numpy.zeros(N,)
hx = numpy.zeros(N,)
hy = numpy.zeros(N,)
hz = numpy.zeros(N,)
hx2 = numpy.zeros(N,)
hy2 = numpy.zeros(N,)
hz2 = numpy.zeros(N,)
tmp_f=numpy.zeros(M,)
eps = 1e-16
for iter in range(0, maxiter):
print(iter)
tmp_u= u_bold_k - tau_1 * AH(v_k + tmp_f- z_k).flat[...]
u_bar_kp1 = tmp_u - tau_1 *( Gx.getH().dot(w_kx) + Gy.getH().dot(w_ky) + Gz.getH().dot(w_kz) )
# Gx2.getH().dot(w_kx2) + Gy2.getH().dot(w_ky2) + Gz2.getH().dot(w_kz2) )
# sx = Gx.dot(u_bar_kp1)
# sy = Gy.dot(u_bar_kp1)
# s = (sx**2 + sy**2)**0.5
w_kp1x = P_lambda(w_kx + (tau_2/tau_1)*Gx.dot(u_bar_kp1), mu, tau_1)
w_kp1y = P_lambda(w_ky+ (tau_2/tau_1)*Gy.dot(u_bar_kp1), mu, tau_1)
w_kp1z = P_lambda(w_kz+ (tau_2/tau_1)*Gz.dot(u_bar_kp1), mu, tau_1)
# w_kp1x2 = P_lambda(w_kx2+ (tau_2/tau_1)*Gx2.dot(u_bar_kp1), mu, tau_1)
# w_kp1y2 = P_lambda(w_ky2+ (tau_2/tau_1)*Gy2.dot(u_bar_kp1), mu, tau_1)
# w_kp1z2 = P_lambda(w_kz2+ (tau_2/tau_1)*Gz2.dot(u_bar_kp1), mu, tau_1)
# hx = (sx+eps)/(s+eps)*Gx.getH().dot(w_kp1)
# hy = (sy+eps)/(s+eps)*Gy.getH().dot(w_kp1)
u_bold_kp1 = tmp_u - tau_1 *( Gx.getH().dot(w_kp1x) + Gy.getH().dot(w_kp1y) + Gz.getH().dot(w_kp1z))
# Gx2.getH().dot(w_kp1x2) + Gy2.getH().dot(w_kp1y2) + Gz2.getH().dot(w_kp1z2))
tmp_f=A(numpy.reshape( u_bold_kp1, Nd))
z_kp1 = Q_f_eps(tmp_f + v_k, f, eps)
v_kp1 = v_k + delta * (tmp_f - z_kp1)
w_kx = w_kp1x
w_ky = w_kp1y
w_kz = w_kp1z
# w_kx2 = w_kp1x2
# w_ky2 = w_kp1y2
# w_kz2 = w_kp1z2
u_bold_k = u_bold_kp1
v_k = v_kp1
z_k = z_kp1
return numpy.reshape(u_bar_kp1, Nd)
import pkg_resources
DATA_PATH = pkg_resources.resource_filename('pynufft', './src/data/')
image = numpy.load(DATA_PATH +'phantom_3D_128_128_128.npz')['arr_0']#[0::2, 0::2, 0::2]
image = numpy.array(image, order='C')
# image = numpy.load('/home/sram/UCL/DATA/G/2 McwBra DICOM/CScontNoECG_DICOM/3D_volume.npz')['arr_0']
# image = image/numpy.max(abs(image.ravel()))
# image = image[32:32+128, 32:32+128,12:12+64]
# image = numpy.abs(image)
# print(special_license)
# pyplot.imshow(numpy.abs(image[:,:,64]), label='original signal',cmap=gray)
# pyplot.show()
Nd = (128,128,128) # time grid, tuple
Kd = (256,256,256) # frequency grid, tuple
Jd = (6,6,6) # interpolator
mid_slice = int(Nd[2]/2)
# om= numpy.load(DATA_PATH+'om3D.npz')['arr_0']
numpy.random.seed(0)
om = numpy.random.randn(int(5e+5),3)
print(om.shape)
from pynufft import NUFFT_cpu, NUFFT_hsa, NUFFT_hsa_legacy
NufftObj = NUFFT_hsa(API = 'ocl', platform_number = 1, device_number = 0)
NufftObj.plan(om, Nd, Kd, Jd)
# NufftObj.offload(API = 'cuda', platform_number = 0, device_number = 0)
gx = NufftObj.thr.to_device(image.astype(numpy.complex64))
gy =NufftObj.forward(gx)
import time
t0 = time.time()
restore_x2 = GBPDNA_old(NufftObj, gy, maxiter=5)
t1 = time.time()
restore_x = NufftObj.solve(gy,'cg', maxiter=50)
t2 = time.time()
print("GBPDNA time = ", t1 - t0)
print("CG time = ", t2 - t1)
#restore_image1 = NufftObj.solve(kspace,'L1TVLAD', maxiter=300,rho=0.1)
#
# restore_x2 = NufftObj.solve(gy,'L1TVOLS', maxiter=100,rho=0.2)
# tau_1 = 1
# tau_2 = 0.1
pyplot.subplot(1,2,1)
pyplot.imshow(numpy.real(gx.get()[:,:,mid_slice]), label='original signal',cmap=gray)
pyplot.title('original')
#pyplot.subplot(2,2,2)
#pyplot.imshow(numpy.real(restore_image1[:,:,32]), label='L1TVLAD',cmap=gray)
#pyplot.title('L1TVLAD')
pyplot.subplot(1,2,2)
pyplot.imshow(numpy.abs(restore_x2[:,:,mid_slice]), label='L1TVOLS',cmap=gray)
pyplot.title('GBPDNA (500 iterations)')
pyplot.show()
