def example_3D():
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]
pyplot.imshow(numpy.abs(image[:, :, 32]),
label='original signal',
cmap=gray)
pyplot.show()
Nd = (64, 64, 64) # time grid, tuple
Kd = (64, 64, 64) # frequency grid, tuple
Jd = (1, 1, 1) # interpolator
# om= numpy.load(DATA_PATH+'om3D.npz')['arr_0']
om = numpy.random.randn(15120, 3)
print(om.shape)
from pynufft import NUFFT_cpu, NUFFT_hsa
NufftObj = NUFFT_cpu()
NufftObj.plan(om, Nd, Kd, Jd)
kspace = NufftObj.forward(image)
restore_image = NufftObj.solve(kspace, 'cg', maxiter=200)
# restore_image1 = NufftObj.solve(kspace,'L1TVLAD', maxiter=200,rho=0.1)
#
restore_image2 = NufftObj.solve(kspace, 'L1TVOLS', maxiter=200, rho=0.1)
pyplot.subplot(2, 2, 1)
pyplot.imshow(numpy.abs(image[:, :, 32]),
label='original signal',
cmap=gray)
pyplot.title('original')
# pyplot.subplot(2,2,2)
# pyplot.imshow(numpy.abs(restore_image1[:,:,32]), label='L1TVLAD',cmap=gray)
# pyplot.title('L1TVLAD')
pyplot.subplot(2, 2, 3)
pyplot.imshow(numpy.abs(restore_image2[:, :, 32]),
label='L1TVOLS',
cmap=gray)
pyplot.title('L1TVOLS')
pyplot.subplot(2, 2, 4)
pyplot.imshow(numpy.abs(restore_image[:, :, 32]), label='CG', cmap=gray)
pyplot.title('CG')
# pyplot.legend([im1, im im4])
pyplot.show()
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
def non_uniform_fft(pos_stack,pos_wavefun,solver,interp_size):
assert len(pos_wavefun.shape) == 2
NufftObj = NUFFT_cpu()
om = pos_stack
Nd = (len(pos_stack[0]),len(pos_stack[1]))
Kd = Nd
Jd = (interp_size,interp_size)
NufftObj.plan(om,Nd,Kd,Jd)
y = NufftObj.forward(pos_wavefun)
mom_wavefun_1 = NufftObj.solve(y,solver=solver )
#mom_wavefun_2 = NufftObj.adjoint(y)
return mom_wavefun_1 #, mom_wavefun_2
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()
NufftObj.plan(om, Nd, Kd, Jd)
time_data = numpy.zeros(256, )
time_data[64:192] = 1.0
pyplot.plot(time_data)
pyplot.ylim(-1,2)
pyplot.show()
nufft_freq_data =NufftObj.forward(time_data)
restore_time = NufftObj.solve(nufft_freq_data,'cg', maxiter=30)
restore_time2 = NufftObj.solve(nufft_freq_data,'L1TVOLS', maxiter=30,rho=1)
im1,=pyplot.plot(numpy.abs(time_data),'r',label='original signal')
# im2,=pyplot.plot(numpy.abs(restore_time1),'b:',label='L1TVLAD')
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, im3,im4])
pyplot.show()
def test_cuda():
import numpy
import matplotlib.pyplot
# load example image
import pkg_resources
## Define the source of data
DATA_PATH = pkg_resources.resource_filename('pynufft', 'src/data/')
# PHANTOM_FILE = pkg_resources.resource_filename('pynufft', 'data/phantom_256_256.txt')
import scipy
image = scipy.misc.ascent()
image = scipy.misc.imresize(image, (256, 256))
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 as M * 2 array
om = numpy.load(DATA_PATH + 'om2D.npz')['arr_0']
# Show the shape of om
print('the shape of om = ', om.shape)
# initiating NUFFT_cpu object
nfft = NUFFT_cpu() # CPU NUFFT class
# Plan the nfft object
nfft.plan(om, Nd, Kd, Jd)
# initiating NUFFT_hsa object
NufftObj = NUFFT_hsa('cuda', 0, 0)
# Plan the NufftObj (similar to NUFFT_cpu)
NufftObj.plan(om, Nd, Kd, Jd)
import time
t0 = time.time()
for pp in range(0, 10):
y = nfft.forward(image)
t_cpu = (time.time() - t0) / 10.0
## Moving image to gpu
## gx is an gpu array, dtype = complex64
gx = NufftObj.to_device(image)
t0 = time.time()
for pp in range(0, 100):
gy = NufftObj.forward(gx)
t_cu = (time.time() - t0) / 100
print('t_cpu = ', t_cpu)
print('t_cuda =, ', t_cu)
print('gy close? = ',
numpy.allclose(y, gy.get(), atol=numpy.linalg.norm(y) * 1e-3))
print("acceleration=", t_cpu / t_cu)
maxiter = 100
import time
t0 = time.time()
x_cpu_cg = nfft.solve(y, 'cg', maxiter=maxiter)
# x2 = nfft.solve(y2, 'L1TVLAD',maxiter=maxiter, rho = 2)
t1 = time.time() - t0
# gy=NufftObj.thr.copy_array(NufftObj.thr.to_device(y2))
t0 = time.time()
x_cuda_cg = NufftObj.solve(gy, 'cg', maxiter=maxiter)
# x = NufftObj.solve(gy,'L1TVLAD', maxiter=maxiter, rho=2)
t2 = time.time() - t0
print(t1, t2)
print('acceleration of cg=', t1 / t2)
t0 = time.time()
x_cpu_TV = nfft.solve(y, 'L1TVOLS', maxiter=maxiter, rho=2)
t1 = time.time() - t0
t0 = time.time()
x_cuda_TV = NufftObj.solve(gy, 'L1TVOLS', maxiter=maxiter, rho=2)
t2 = time.time() - t0
print(t1, t2)
print('acceleration of TV=', t1 / t2)
matplotlib.pyplot.subplot(2, 2, 1)
matplotlib.pyplot.imshow(x_cpu_cg.real, cmap=matplotlib.cm.gray)
matplotlib.pyplot.title('CG_cpu')
matplotlib.pyplot.subplot(2, 2, 2)
matplotlib.pyplot.imshow(x_cuda_cg.get().real, cmap=matplotlib.cm.gray)
matplotlib.pyplot.title('CG_cuda')
matplotlib.pyplot.subplot(2, 2, 3)
matplotlib.pyplot.imshow(x_cpu_TV.real, cmap=matplotlib.cm.gray)
matplotlib.pyplot.title('TV_cpu')
matplotlib.pyplot.subplot(2, 2, 4)
matplotlib.pyplot.imshow(x_cuda_TV.get().real, cmap=matplotlib.cm.gray)
matplotlib.pyplot.title('TV_cuda')
matplotlib.pyplot.show()
NufftObj.release()
del NufftObj
Jd = (6,6) # interpolator size NufftObj.plan(om, Nd, Kd, Jd) # load image from scipy.misc.face() import scipy.misc import matplotlib.cm as cm image = scipy.misc.face(gray=True) image = scipy.misc.imresize(image, (256,256)) image=image.astype(numpy.float)/numpy.max(image[...]) pyplot.imshow(image, cmap=cm.gray) pyplot.show() # Forward NUFFT transform y = NufftObj.forward(image) # Adjoint NUFFT k = NufftObj.y2k(y) import matplotlib.colors k_show = numpy.fft.fftshift(k) pyplot.imshow(numpy.abs(k_show), cmap=cm.gray, norm=matplotlib.colors.Normalize(0, 1e+3)) pyplot.show() # Inverse transform using density compensation inverse_DC() x3 = NufftObj.inverse_DC(y) x3_display = x3*1.0/numpy.max(x3[...].real) pyplot.imshow(x3_display.real,cmap=cm.gray) pyplot.show()
Nd = (256, ) # time grid, tuple
Kd = (512, ) # frequency grid, tuple
Jd = (7, ) # interpolator
NufftObj = NUFFT_cpu()
NufftObj.plan(om, Nd, Kd, Jd)
time_data = numpy.zeros(256, )
time_data[64:192] = 1.0
pyplot.plot(time_data)
pyplot.ylim(-1, 2)
pyplot.show()
nufft_freq_data = NufftObj.forward(time_data)
pyplot.plot(om, nufft_freq_data.real, '.', label='real')
pyplot.plot(om, nufft_freq_data.imag, 'r.', label='imag')
pyplot.legend()
pyplot.show()
restore_time = NufftObj.solve(nufft_freq_data, 'cg', maxiter=30)
restore_time1 = NufftObj.solve(nufft_freq_data, 'L1TVLAD', 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')
im2, = pyplot.plot(numpy.abs(restore_time1), 'b:', label='L1TVLAD')
im3, = pyplot.plot(numpy.abs(restore_time2), 'k--', label='L1TVOLS')
im4, = pyplot.plot(numpy.abs(restore_time),
'r:',
label='conjugate_gradient_method')
results.append(result)
# Now enter the second process
# This is the standard multiprocessing Pool
D = atomic_NUFFT(om2, Nd, Kd, Jd, 'cuda', 0)
# Non-obstructive
result = pool.apply_async(D.run, args = (x, 1))
results.append(result)
# closing the pool
pool.close()
pool.join()
# results are appended
# Now print the outputs
result1 = results[0].get()
result2 = results[1].get()
# check CPU results
NUFFT_cpu1 = NUFFT_cpu()
NUFFT_cpu1.plan(om1, Nd, Kd, Jd)
y1 = NUFFT_cpu1.forward(x)
print('norm = ', numpy.linalg.norm(y1 - result1) / numpy.linalg.norm(y1))
NUFFT_cpu2 = NUFFT_cpu()
NUFFT_cpu2.plan(om2, Nd, Kd, Jd)
y2 = NUFFT_cpu2.forward(x)
print('norm = ', numpy.linalg.norm(y2 - result2) / numpy.linalg.norm(y2))
import numpy from pynufft import NUFFT_cpu import scipy.misc import matplotlib Nd = (256, 256) Kd = (512, 512) Jd = (6, 6) om = numpy.random.randn(65536, 2) x = scipy.misc.imresize(scipy.misc.ascent(), Nd) om1 = om[om[:, 0] > 0, :] om2 = om[om[:, 0] <= 0, :] NufftObj1 = NUFFT_cpu() NufftObj1.plan(om1, Nd, Kd, Jd) NufftObj2 = NUFFT_cpu() NufftObj2.plan(om2, Nd, Kd, Jd) y1 = NufftObj1.forward(x) y2 = NufftObj2.forward(x)
pyplot.imshow(numpy.abs(image[:, :, 32]), label='original signal', cmap=gray)
pyplot.show()
Nd = (64, 64, 64) # time grid, tuple
Kd = (64, 64, 64) # frequency grid, tuple
Jd = (1, 1, 1) # interpolator
# om= numpy.load(DATA_PATH+'om3D.npz')['arr_0']
om = numpy.random.randn(151200, 3) * 2
print(om.shape)
from pynufft import NUFFT_cpu, NUFFT_hsa
NufftObj = NUFFT_cpu()
NufftObj.plan(om, Nd, Kd, Jd)
kspace = NufftObj.forward(image)
restore_image = NufftObj.solve(kspace, 'cg', maxiter=500)
restore_image1 = NufftObj.solve(kspace, 'L1TVLAD', maxiter=500, rho=0.1)
#
restore_image2 = NufftObj.solve(kspace, 'L1TVOLS', maxiter=500, rho=0.1)
pyplot.subplot(2, 2, 1)
pyplot.imshow(numpy.real(image[:, :, 32]), 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(2, 2, 3)
pyplot.imshow(numpy.real(restore_image2[:, :, 32]), label='L1TVOLS', cmap=gray)
fake_coil = create_fake_coils(Nd[0], Nc)
H = numpy.ones(Nd + (Nc, ), dtype=numpy.complex)
for pp in range(0, Nc):
H[..., pp] = fake_coil[pp]
H2 = H * numpy.reshape(M0, (256, 256, 1))
H = Nd_sense(H2, maxiter=20, sigma=100)
H = H - numpy.min(abs(H.ravel()))
# matplotlib.pyplot.imshow(H[:,:,0].real)
# matplotlib.pyplot.show()
# H = H*numpy.reshape(M0, Nd+(1,))*(1.0+0.0j)/256
NufftObj_coil.plan1(om2, Nd, (512, 512), (5, 5), ft_axes=(0, 1), coil_sense=H)
y = NufftObj.forward(M0)
y2 = numpy.fft.fftshift(
numpy.fft.ifft2(numpy.fft.fftshift(y.reshape(Nd, order='C'))))
y3 = NufftObj_coil.forward((M0) * (1.0 + 0.0j))
print(y3.shape, y3)
# y3 = y3.reshape((Nc, 256, 256), order='C')
# y4 = numpy.einsum('ijk -> jki', y3)
y4 = y3.reshape((256, 256, Nc), order='C')
# y4 = numpy.fft.fftshift(numpy.fft.ifftn(numpy.fft.fftshift(y3, axes = (1,2)), axes = (1,2)), axes = (1,2))
y4 = numpy.fft.fftshift(numpy.fft.ifftn(numpy.fft.fftshift(y4, axes=(0, 1)),
axes=(0, 1)),
axes=(0, 1))
# y2 = NufftObj.adjoint(y) / 512
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")
NufftObj.plan(om, Nd, Kd, Jd) # Now test 1D case import matplotlib.pyplot as pyplot # Now build a box function time_data = numpy.zeros(256, ) time_data[96:128 + 32] = 1.0 # 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()
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()[::2, ::2]
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)
# 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()
image4 = NufftObj.solve(y, 'L1TVOLS', maxiter=100, rho=1)
image2 = NufftObj.solve(y, 'dc', maxiter=25)
image3 = NufftObj.solve(y, 'cg', maxiter=25)
matplotlib.pyplot.subplot(1, 3, 1)
matplotlib.pyplot.imshow(image2.real,
cmap=matplotlib.cm.gray,
norm=matplotlib.colors.Normalize(vmin=0.0,
vmax=1))
matplotlib.pyplot.title('dc')
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.title('cg')
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.title('L1TVOLS')
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', '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()
print('setting spectrum dimension Kd...', Kd)
Jd = (6, 6) # interpolation size
print('setting interpolation size Jd...', Jd)
NufftObj.plan(om, Nd, Kd, Jd)
image = scipy.misc.ascent()
image = scipy.misc.imresize(image, (256, 256))
image = image * 1.0 / numpy.max(image[...])
print('loading image...')
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))
def FFTgridDSGfile(netCDFfiles):
ds = Dataset(netCDFfiles[1], 'a')
vs = ds.get_variables_by_attributes(standard_name='sea_water_pressure_due_to_sea_water')
vs = ds.get_variables_by_attributes(long_name='actual depth')
pres_var = vs[0]
pres = pres_var[:]
#plt.plot(pres)
#plt.show()
temp_var = ds.variables["TEMP"]
print("Read and convert time")
time_var = ds.variables["TIME"]
#time = num2date(time_var[:], units=time_var.units, calendar=time_var.calendar)
#first_hour = time[0].replace(minute=0, second=0, microsecond=0)
t = time_var[:] * 24
hours = t
# scale time to -pi to pi
hours_min = np.min(hours)
hours_max = np.max(hours)
mid_hours = (hours_max + hours_min)/2
print("time min, max", hours_min, hours_max, num2date(hours_max/24, units=time_var.units, calendar=time_var.calendar), num2date(hours_min/24, units=time_var.units, calendar=time_var.calendar), num2date(mid_hours/24, units=time_var.units, calendar=time_var.calendar))
t2pi = 2*np.pi * (hours - mid_hours) / (hours_max - hours_min)
# scale pressure to -pi to pi
pres_min = np.min(pres)
pres_max = np.max(pres)
pres_mid = (pres_max + pres_min)/2
print("pres min, max", pres_min, pres_max, pres_mid)
d2pi = 2*np.pi * (pres - pres_mid) / (pres_max - pres_min)
#plt.plot(t2pi)
#plt.show()
nt_points = int(hours_max - hours_min)
nd_points = 20
print(nt_points, nd_points)
print("Calc FFT")
x = t2pi
y = d2pi
c = np.array(temp_var[:])
#c.real = temp_var[:]
#c.imag = 0
print(c)
print("size ", len(x), len(y), len(c))
# Provided om, the size of time series (Nd), oversampled grid (Kd), and interpolatro size (Jd)
om = [x, y]
Nd = (256, 256) # image size
Kd = (512, 512) # k-space size
Jd = (6, 6) # interpolation size
NufftObj = NUFFT_cpu()
NufftObj.plan(om, Nd, Kd, Jd)
fft = NufftObj.forward(c)
print("fft ")
print(fft)
for x in range(0, nd_points):
plt.plot(10*np.log10(abs(fft[:,x])))
plt.grid(True)
plt.show()
F1 = np.fft.ifft2(fft)
f2 = np.fft.fftshift(F1)
print("inverted ", f2.shape, len(hours))
first_hour = num2date(hours_min/24, units=time_var.units, calendar=time_var.calendar).replace(minute=0, second=0, microsecond=0)
td = [first_hour + timedelta(hours=x) for x in range(nt_points)]
for x in range(0, nd_points):
plt.plot(td, abs(f2[:,x])/(len(hours)/(nt_points)))
plt.grid(True)
plt.xticks(fontsize=6)
plt.show()
index_var = ds.variables["instrument_index"]
idx = index_var[:]
instrument_id_var = ds.variables["instrument_id"]
#time = num2date(time_var[:], units=time_var.units, calendar=time_var.calendar)
#print(idx)
i = 0
for x in chartostring(instrument_id_var[:]):
#print (i, x, time[idx == 1], pres[idx == i])
#plt.plot(time[idx == i], pres[idx == i]) # , marker='.'
i += 1
#plt.gca().invert_yaxis()
#plt.grid(True)
# close the netCDF file
ds.close()
plt.show()
ncOut = Dataset("fft-bin.nc", 'w', format='NETCDF4')
# add time
tDim = ncOut.createDimension("TIME", nt_points)
ncTimesOut = ncOut.createVariable("TIME", "d", ("TIME",), zlib=True)
ncTimesOut.long_name = "time"
ncTimesOut.units = "days since 1950-01-01 00:00:00 UTC"
ncTimesOut.calendar = "gregorian"
ncTimesOut.axis = "T"
ncTimesOut[:] = hours_min / 24
bin_dim = ncOut.createDimension("BIN", nd_points)
bin_var = ncOut.createVariable("BIN", "d", ("BIN",), zlib=True)
bin_var[:] = range(0, nd_points)
# add variables
nc_var_out = ncOut.createVariable("TEMP", "f4", ("TIME", "BIN"), fill_value=np.nan, zlib=True)
print("shape ", f2.shape, nc_var_out.shape)
nc_var_out[:] = abs(f2)
# add some summary metadata
ncTimeFormat = "%Y-%m-%dT%H:%M:%SZ"
# add creating and history entry
ncOut.setncattr("date_created", datetime.utcnow().strftime(ncTimeFormat))
ncOut.setncattr("history", datetime.utcnow().strftime("%Y-%m-%d") + " created from file " + netCDFfiles[1])
ncOut.close()
