def example_1D():
om = numpy.random.randn(1512, 1)
# print(om)
# print(om.shape)
# pyplot.hist(om)
# pyplot.show()
Nd = (256, ) # time grid, tuple
Kd = (512, ) # frequency grid, tuple
Jd = (7, ) # interpolator
from pynufft import NUFFT_cpu, NUFFT_hsa
NufftObj = NUFFT_cpu()
batch = 4
NufftObj.plan(om, Nd, Kd, Jd, batch=batch)
time_data = numpy.zeros((256, batch))
time_data[64:192, :] = 1.0
pyplot.plot(time_data)
pyplot.ylim(-1, 2)
pyplot.show()
nufft_freq_data = NufftObj.forward(time_data)
print('shape of y = ', nufft_freq_data.shape)
x2 = NufftObj.adjoint(nufft_freq_data)
restore_time = NufftObj.solve(nufft_freq_data, 'cg', maxiter=30)
restore_time1 = NufftObj.solve(nufft_freq_data,
'L1TVOLS',
maxiter=30,
rho=1)
#
# restore_time2 = NufftObj.solve(nufft_freq_data,'L1TVOLS', maxiter=30,rho=1)
#
# im1,=pyplot.plot(numpy.abs(time_data),'r',label='original signal')
# im3,=pyplot.plot(numpy.abs(restore_time2),'k--',label='L1TVOLS')
# im4,=pyplot.plot(numpy.abs(restore_time),'r:',label='conjugate_gradient_method')
# pyplot.legend([im1, im2, im3,im4])
for slice in range(0, batch):
pyplot.plot(numpy.abs(x2[:, slice]))
pyplot.plot(numpy.abs(restore_time[:, slice]))
pyplot.show()
def performUndersampling(fullImgVol,
om=None,
dcf=None,
interpolationSize4NUFFT=6,
complex2real=np.abs,
ommatpath=None):
#Either send om and dcf, or ommatpath.
#path will only be used in om not supplied
if om is None:
temp_mat = sio.loadmat(ommatpath)
om = temp_mat['om']
dcf = temp_mat['dcf'].squeeze()
imageSize = fullImgVol.shape[0]
baseresolution = imageSize * 2
NufftObj = NUFFT_cpu()
Nd = (baseresolution, baseresolution) # image size
Kd = (baseresolution * 2, baseresolution * 2) # k-space size
Jd = (interpolationSize4NUFFT, interpolationSize4NUFFT
) # interpolation size
NufftObj.plan(om, Nd, Kd, Jd)
underImgVol = np.zeros(fullImgVol.shape, dtype=fullImgVol.dtype)
for i in range(fullImgVol.shape[-1]):
oversam_fully = np.zeros((baseresolution, baseresolution),
dtype=fullImgVol.dtype)
oversam_fully[imageSize // 2:imageSize + imageSize // 2, imageSize //
2:imageSize + imageSize // 2] = fullImgVol[..., i]
y = NufftObj.forward(oversam_fully)
y = np.multiply(dcf, y)
oversam_under = NufftObj.adjoint(y)
underImgVol[..., i] = complex2real(
oversam_under[imageSize // 2:imageSize + imageSize // 2,
imageSize // 2:imageSize + imageSize // 2])
return underImgVol
matplotlib.pyplot.imshow(image.real, cmap=matplotlib.cm.gray)
matplotlib.pyplot.show()
y = NufftObj.forward(image)
print('setting non-uniform data')
print('y is an (M,) list', type(y), y.shape)
matplotlib.pyplot.subplot(2, 2, 1)
image0 = NufftObj.solve(y, solver='cg', maxiter=50)
matplotlib.pyplot.title('Restored image (cg)')
matplotlib.pyplot.imshow(image0.real,
cmap=matplotlib.cm.gray,
norm=matplotlib.colors.Normalize(vmin=0.0, vmax=1))
matplotlib.pyplot.subplot(2, 2, 2)
image2 = NufftObj.adjoint(y)
matplotlib.pyplot.imshow(image2.real,
cmap=matplotlib.cm.gray,
norm=matplotlib.colors.Normalize(vmin=0.0, vmax=5))
matplotlib.pyplot.title('Adjoint transform')
matplotlib.pyplot.subplot(2, 2, 3)
image3 = NufftObj.solve(y, solver='L1TVOLS', maxiter=50, rho=0.1)
matplotlib.pyplot.title('L1TV OLS')
matplotlib.pyplot.imshow(image3.real,
cmap=matplotlib.cm.gray,
norm=matplotlib.colors.Normalize(vmin=0.0, vmax=1))
matplotlib.pyplot.subplot(2, 2, 4)
image4 = NufftObj.solve(y, solver='L1TVLAD', maxiter=50, rho=0.1)
matplotlib.pyplot.title('L1TV LAD')
for x in range (-N, N):
for y in range(-N, N):
img[x-N, y-N] = img[x-N,y-N] + X * cmath.exp(-2j*math.pi * (u*x + v*y))
u0 = 0.05
v0 = 0.013
u1 = 0.0018
v1 = 0.046
img = np.zeros([32,32], dtype=np.complex128)
expectedIFT(img, 3, u0, v0)
expectedIFT(img, 2.5, u1, v1)
plt.imshow(np.real(img))
print(np.max(np.real(img)))
NufftObj = NUFFT_cpu()
Nd = (32, 32) # image size
Kd = (64, 64) # k-space size
Jd = (2, 2) # interpolation size
om = [
[u0, v0],
[u1,v1]]
NufftObj.plan(np.asarray(om), Nd, Kd, Jd)
img2 = NufftObj.adjoint([3, 2.5])
plt.imshow(np.real(img2))
print(np.max(np.real(img2)))
om[512 * index:512 * (index + 1), 1] = spoke_y
#plt.plot(om[:,0], om[:,1],'.')
#plt.title("Radial Kspace Trajectory")
#plt.show()
numProjections = kspace.shape[1]
numReadouts = kspace.shape[0]
print('Number of Projections = ', numProjections)
print('Number of Readout Values = ', numReadouts)
myNufft = NUFFT_cpu()
myNufft.plan(om=om, Nd=(256, 256), Kd=(numReadouts, numReadouts), Jd=(2, 2))
y = kspace.flatten(order='C')
image = myNufft.adjoint(y)
#y = myNufft.forward(image)
#ipdb.set_trace()
plt.subplot(2, 2, 1)
image0 = myNufft.solve(y, solver='cg', maxiter=50)
#img = image0.real/image0.real.max()
plt.title('Restored image (cg)')
plt.imshow(image0.real,
cmap=matplotlib.cm.gray,
norm=matplotlib.colors.Normalize(vmin=0.0, vmax=1))
plt.show()
# -*- coding: utf-8 -*-
"""
Created on Mon Oct 29 08:39:01 2018
@author: jon
"""
import cmath
import math
import numpy as np
import matplotlib.pyplot as plt
from pynufft import NUFFT_cpu
import scipy.io as sio
y = sio.loadmat("/home/jon/Desktop/export_mat/y.mat")['y'][0,0].reshape(307780)
p = np.asarray(sio.loadmat("/home/jon/Desktop/export_mat/p.mat")["p"])
dirty = np.asarray(sio.loadmat("/home/jon/Desktop/export_mat/dirty.mat")["dirty"])
NufftObj = NUFFT_cpu()
Nd = (512, 512) # image size
Kd = (2048, 2048) # k-space size
Jd = (8, 8) # interpolation size
NufftObj.plan(p, Nd, Kd, Jd)
res = NufftObj.adjoint(y)
#res = NufftObj.solve(y, solver='cg',maxiter=1000)
plt.imshow(np.real(res[256:640,256:640]))
matplotlib.pyplot.imshow(image.real, cmap=matplotlib.cm.gray)
matplotlib.pyplot.show()
y = NufftObj.forward(image)
print('setting non-uniform data')
print('y is an (M,) list', type(y), y.shape)
matplotlib.pyplot.subplot(2, 2, 1)
image0 = NufftObj.solve(y, solver='cg', maxiter=50)
matplotlib.pyplot.title('Restored image (cg)')
matplotlib.pyplot.imshow(image0.real,
cmap=matplotlib.cm.gray,
norm=matplotlib.colors.Normalize(vmin=0.0, vmax=1))
matplotlib.pyplot.subplot(2, 2, 2)
image2 = NufftObj.adjoint(y)
matplotlib.pyplot.imshow(image2.real,
cmap=matplotlib.cm.gray,
norm=matplotlib.colors.Normalize(vmin=0.0, vmax=5))
matplotlib.pyplot.title('Adjoint transform')
matplotlib.pyplot.subplot(2, 2, 3)
image3 = NufftObj.solve(y, solver='L1TVOLS', maxiter=50, rho=0.1)
matplotlib.pyplot.title('L1TV OLS')
matplotlib.pyplot.imshow(image3.real,
cmap=matplotlib.cm.gray,
norm=matplotlib.colors.Normalize(vmin=0.0, vmax=1))
matplotlib.pyplot.subplot(2, 2, 4)
image4 = NufftObj.solve(y, solver='L1TVLAD', maxiter=50, rho=0.1)
matplotlib.pyplot.title('L1TV LAD')
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()
def test_init():
# cm = matplotlib.cm.gray
# load example image
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
import scipy
image = scipy.misc.ascent()[::2,::2]
image=image.astype(numpy.float)/numpy.max(image[...])
Nd = (256, 256) # image space size
Kd = (512, 512) # k-space size
Jd = (6,6) # interpolation size
# load k-space points
om = numpy.load(DATA_PATH+'om2D.npz')['arr_0']
nfft = NUFFT_cpu() # CPU
nfft.plan(om, Nd, Kd, Jd)
try:
NufftObj = NUFFT_hsa('cuda',0,0)
except:
NufftObj = NUFFT_hsa('ocl',0,0)
# NufftObj2 = NUFFT_hsa('cuda',0,0)
NufftObj.debug = 1
NufftObj.plan(om, Nd, Kd, Jd, radix=2)
# NufftObj2.plan(om, Nd, Kd, Jd)
# NufftObj.offload(API = 'cuda', platform_number = 0, device_number = 0)
# NufftObj2.offload(API = 'cuda', platform_number = 0, device_number = 0)
# NufftObj2.offload('cuda')
# NufftObj.offload(API = 'cuda', platform_number = 0, device_number = 0)
# print('api=', NufftObj.thr.api_name())
# NufftObj.offload(API = 'ocl', platform_number = 0, device_number = 0)
y = nfft.k2y(nfft.xx2k(nfft.x2xx(image)))
NufftObj.x_Nd = NufftObj.thr.to_device( image.astype(dtype))
gx = NufftObj.thr.copy_array(NufftObj.x_Nd)
print('x close? = ', numpy.allclose(image, gx.get() , atol=1e-4))
gxx = NufftObj.x2xx(gx)
print('xx close? = ', numpy.allclose(nfft.x2xx(image), gxx.get() , atol=1e-4))
gk = NufftObj.xx2k(gxx)
k = nfft.xx2k(nfft.x2xx(image))
print('k close? = ', numpy.allclose(nfft.xx2k(nfft.x2xx(image)), gk.get(), atol=1e-3*numpy.linalg.norm(k)))
gy = NufftObj.k2y(gk)
k2 = NufftObj.y2k(gy)
print('y close? = ', numpy.allclose(y, gy.get() , atol=1e-3*numpy.linalg.norm(y)), numpy.linalg.norm((y - gy.get())/numpy.linalg.norm(y)))
y2 = y
print('k2 close? = ', numpy.allclose(nfft.y2k(y2), k2.get(), atol=1e-3*numpy.linalg.norm(nfft.y2k(y2)) ), numpy.linalg.norm(( nfft.y2k(y2)- k2.get())/numpy.linalg.norm(nfft.y2k(y2))))
gxx2 = NufftObj.k2xx(k2)
# print('xx close? = ', numpy.allclose(nfft.k2xx(nfft.y2k(y2)), NufftObj.xx_Nd.get(queue=NufftObj.queue, async=False) , atol=0.1))
gx2 = NufftObj.xx2x(gxx2)
print('x close? = ', numpy.allclose(nfft.adjoint(y2), gx2.get() , atol=1e-3*numpy.linalg.norm(nfft.adjoint(y2))))
image3 = gx2.get()
import time
t0 = time.time()
# k = nfft.xx2k(nfft.x2xx(image))
for pp in range(0,50):
# y = nfft.k2y(nfft.xx2k(nfft.x2xx(image)))
y = nfft.forward(image)
# y = nfft.k2y(k)
# k = nfft.y2k(y)
# x = nfft.adjoint(y)
# y = nfft.forward(image)
# y2 = NufftObj.y.get( NufftObj.queue, async=False)
t_cpu = (time.time() - t0)/50.0
print(t_cpu)
# del nfft
gy2=NufftObj.forward(gx)
# gk = NufftObj.xx2k(NufftObj.x2xx(gx))
t0= time.time()
for pp in range(0,20):
# pass
gy2 = NufftObj.forward(gx)
# gy2 = NufftObj.k2y(gk)
# gx2 = NufftObj.adjoint(gy2)
# gk2 = NufftObj.y2k(gy2)
# del gy2
# c = gx2.get()
# gy=NufftObj.forward(gx)
NufftObj.thr.synchronize()
t_cl = (time.time() - t0)/20
print(t_cl)
print('gy close? = ', numpy.allclose(y, gy.get(), atol=numpy.linalg.norm(y)*1e-3))
print("acceleration=", t_cpu/t_cl)
maxiter =100
import time
t0= time.time()
# x2 = nfft.solve(y2, 'cg',maxiter=maxiter)
x2 = nfft.solve(y2, 'L1TVOLS',maxiter=maxiter, rho = 2)
t1 = time.time()-t0
# gy=NufftObj.thr.copy_array(NufftObj.thr.to_device(y2))
t0= time.time()
# x = NufftObj.solve(gy,'cg', maxiter=maxiter)
x = NufftObj.solve(gy,'L1TVOLS', maxiter=maxiter, rho=2)
t2 = time.time() - t0
print(t1, t2)
print('acceleration=', t1/t2 )
# k = x.get()
# x = nfft.k2xx(k)/nfft.st['sn']
# return
try:
import matplotlib.pyplot
matplotlib.pyplot.subplot(1, 2, 1)
matplotlib.pyplot.imshow( x.get().real, cmap= matplotlib.cm.gray, vmin = 0, vmax = 1)
matplotlib.pyplot.title("HSA reconstruction")
matplotlib.pyplot.subplot(1, 2,2)
matplotlib.pyplot.imshow(x2.real, cmap= matplotlib.cm.gray)
matplotlib.pyplot.title("CPU reconstruction")
matplotlib.pyplot.show(block = False)
matplotlib.pyplot.pause(3)
matplotlib.pyplot.close()
# del NufftObj.thr
# del NufftObj
except:
print("no graphics")
# Now display the function pyplot.plot(time_data) pyplot.ylim(-1, 2) pyplot.show() # Forward NUFFT y = NufftObj.forward(time_data) # Display the nonuniform spectrum pyplot.plot(om, y.real, '.', label='real') pyplot.plot(om, y.imag, 'r.', label='imag') pyplot.legend() pyplot.show() # Adjoint NUFFT x2 = NufftObj.adjoint(y) pyplot.plot(x2.real, '.-', label='real') pyplot.plot(x2.imag, 'r.-', label='imag') pyplot.plot(time_data, 'k', label='original signal') pyplot.ylim(-1, 2) pyplot.legend() pyplot.show() # Test inverse method using density compensation (inverse DC) x3 = NufftObj.inverse_DC(y) pyplot.plot(x3.real, '.-', label='real') pyplot.plot(x3.imag, 'r.-', label='imag') pyplot.plot(time_data, 'k', label='original signal') pyplot.ylim(-1, 2) pyplot.legend() pyplot.show()
