def gpuGridrec(tomo,angles,center,input_params):
"""
Gridrec reconstruction using GPU based gridding
Inputs: tomo : 3D numpy sinogram array with dimensions same as tomopy
angles : Array of angles in radians
center : Floating point center of rotation
input_params : A dictionary with the keys
'gpu_device' : Device id of the gpu (For a 4 GPU cluster ; 0-3)
'oversamp_factor': A factor by which to pad the image/data for FFT
'fbp_filter_param' : A number between 0-1 for setting the filter cut-off for FBP
"""
print('Starting GPU NUFFT recon')
#allocate space for final answer
af.set_device(input_params['gpu_device']) #Set the device number for gpu based code
#Change tomopy format
new_tomo=np.transpose(tomo,(1,2,0)) #slice, columns, angles
im_size = new_tomo.shape[1]
num_slice = new_tomo.shape[0]
num_angles=new_tomo.shape[2]
pad_size=np.int16(im_size*input_params['oversamp_factor'])
# nufft_scaling = (np.pi/pad_size)**2
#Initialize structures for NUFFT
sino={}
geom={}
sino['Ns'] = pad_size#Sinogram size after padding
sino['Ns_orig'] = im_size #size of original sinogram
sino['center'] = center + (sino['Ns']/2 - sino['Ns_orig']/2) #for padded sinogram
sino['angles'] = angles
sino['filter'] = input_params['fbp_filter_param'] #Paramter to control strength of FBP filter normalized to [0,1]
#Initialize NUFFT parameters
nufft_params = init_nufft_params(sino,geom)
rec_nufft = afnp.zeros((num_slice/2,sino['Ns_orig'],sino['Ns_orig']),dtype=afnp.complex64)
Ax = afnp.zeros((sino['Ns'],num_angles),dtype=afnp.complex64)
pad_idx = slice(sino['Ns']/2-sino['Ns_orig']/2,sino['Ns']/2+sino['Ns_orig']/2)
rec_nufft_final=np.zeros((num_slice,sino['Ns_orig'],sino['Ns_orig']),dtype=np.float32)
#Move all data to GPU
slice_1=slice(0,num_slice,2)
slice_2=slice(1,num_slice,2)
gdata=afnp.array(new_tomo[slice_1]+1j*new_tomo[slice_2],dtype=afnp.complex64)
x_recon = afnp.zeros((sino['Ns'],sino['Ns']),dtype=afnp.complex64)
#loop over all slices
for i in range(0,num_slice/2):
Ax[pad_idx,:]=gdata[i]
#filtered back-projection
rec_nufft[i] = (back_project(Ax,nufft_params))[pad_idx,pad_idx]
#Move to CPU
#Rescale result to match tomopy
rec_nufft=np.array(rec_nufft,dtype=np.complex64) #*nufft_scaling
rec_nufft_final[slice_1]=np.array(rec_nufft.real,dtype=np.float32)
rec_nufft_final[slice_2]=np.array(rec_nufft.imag,dtype=np.float32)
return rec_nufft_final
def gpuGridrec(tomo, angles, center, input_params):
print('Starting GPU NUFFT recon')
#allocate space for final answer
af.set_device(
input_params['gpu_device']) #Set the device number for gpu based code
#Change tomopy format
new_tomo = np.transpose(tomo, (1, 2, 0)) #slice, columns, angles
im_size = new_tomo.shape[1]
num_slice = new_tomo.shape[0]
num_angles = new_tomo.shape[2]
pad_size = np.int16(im_size * input_params['oversamp_factor'])
nufft_scaling = (np.pi / pad_size)**2
#Initialize structures for NUFFT
sino = {}
geom = {}
sino['Ns'] = pad_size #Sinogram size after padding
sino['Ns_orig'] = im_size #size of original sinogram
sino['center'] = center + (sino['Ns'] / 2 - sino['Ns_orig'] / 2
) #for padded sinogram
sino['angles'] = angles
sino['filter'] = input_params[
'fbp_filter_param'] #Paramter to control strength of FBP filter normalized to [0,1]
#Initialize NUFFT parameters
nufft_params = init_nufft_params(sino, geom)
rec_nufft = afnp.zeros((num_slice / 2, sino['Ns_orig'], sino['Ns_orig']),
dtype=afnp.complex64)
Ax = afnp.zeros((sino['Ns'], num_angles), dtype=afnp.complex64)
pad_idx = slice(sino['Ns'] / 2 - sino['Ns_orig'] / 2,
sino['Ns'] / 2 + sino['Ns_orig'] / 2)
rec_nufft_final = np.zeros((num_slice, sino['Ns_orig'], sino['Ns_orig']),
dtype=np.float32)
#Move all data to GPU
slice_1 = slice(0, num_slice, 2)
slice_2 = slice(1, num_slice, 2)
gdata = afnp.array(new_tomo[slice_1] + 1j * new_tomo[slice_2],
dtype=afnp.complex64)
x_recon = afnp.zeros((sino['Ns'], sino['Ns']), dtype=afnp.complex64)
#loop over all slices
for i in range(0, num_slice / 2):
Ax[pad_idx, :] = gdata[i]
#filtered back-projection
rec_nufft[i] = (back_project(Ax, nufft_params))[pad_idx, pad_idx]
#Move to CPU
#Rescale result to match tomopy
rec_nufft = np.array(rec_nufft, dtype=np.complex64) * nufft_scaling
rec_nufft_final[slice_1] = np.array(rec_nufft.real, dtype=np.float32)
rec_nufft_final[slice_2] = np.array(rec_nufft.imag, dtype=np.float32)
return rec_nufft_final
def gpuSIRT(tomo, angles, center, input_params):
print('Starting GPU SIRT recon')
#allocate space for final answer
af.set_device(
input_params['gpu_device']) #Set the device number for gpu based code
#Change tomopy format
new_tomo = np.transpose(tomo, (1, 2, 0)) #slice, columns, angles
im_size = new_tomo.shape[1]
num_slice = new_tomo.shape[0]
num_angles = new_tomo.shape[2]
pad_size = np.int16(im_size * input_params['oversamp_factor'])
nufft_scaling = (np.pi / pad_size)**2
num_iter = input_params['num_iter']
#Initialize structures for NUFFT
sino = {}
geom = {}
sino['Ns'] = pad_size #Sinogram size after padding
sino['Ns_orig'] = im_size #size of original sinogram
sino['center'] = center + (sino['Ns'] / 2 - sino['Ns_orig'] / 2
) #for padded sinogram
sino['angles'] = angles
#Initialize NUFFT parameters
nufft_params = init_nufft_params(sino, geom)
temp_y = afnp.zeros((sino['Ns'], num_angles), dtype=afnp.complex64)
temp_x = afnp.zeros((sino['Ns'], sino['Ns']), dtype=afnp.complex64)
x_recon = afnp.zeros((num_slice / 2, sino['Ns_orig'], sino['Ns_orig']),
dtype=afnp.complex64)
pad_idx = slice(sino['Ns'] / 2 - sino['Ns_orig'] / 2,
sino['Ns'] / 2 + sino['Ns_orig'] / 2)
#allocate output array
rec_sirt_final = np.zeros((num_slice, sino['Ns_orig'], sino['Ns_orig']),
dtype=np.float32)
#Pre-compute diagonal scaling matrices ; one the same size as the image and the other the same as data
#initialize an image of all ones
x_ones = afnp.ones((sino['Ns_orig'], sino['Ns_orig']),
dtype=afnp.complex64)
temp_x[pad_idx, pad_idx] = x_ones
temp_proj = forward_project(temp_x,
nufft_params) * (sino['Ns'] * afnp.pi / 2)
R = 1 / afnp.abs(temp_proj)
R[afnp.isnan(R)] = 0
R[afnp.isinf(R)] = 0
R = afnp.array(R, dtype=afnp.complex64)
#Initialize a sinogram of all ones
y_ones = afnp.ones((sino['Ns_orig'], num_angles), dtype=afnp.complex64)
temp_y[pad_idx] = y_ones
temp_backproj = back_project(temp_y, nufft_params) * nufft_scaling / 2
C = 1 / (afnp.abs(temp_backproj))
C[afnp.isnan(C)] = 0
C[afnp.isinf(C)] = 0
C = afnp.array(C, dtype=afnp.complex64)
#Move all data to GPU
slice_1 = slice(0, num_slice, 2)
slice_2 = slice(1, num_slice, 2)
gdata = afnp.array(new_tomo[slice_1] + 1j * new_tomo[slice_2],
dtype=afnp.complex64)
#loop over all slices
for i in range(num_slice / 2):
for iter_num in range(num_iter):
#filtered back-projection
temp_x[pad_idx, pad_idx] = x_recon[i]
Ax = (np.pi / 2) * sino['Ns'] * forward_project(
temp_x, nufft_params)
temp_y[pad_idx] = gdata[i]
x_recon[i] = x_recon[i] + (
C * back_project(R * (temp_y - Ax), nufft_params) *
nufft_scaling / 2)[pad_idx, pad_idx]
#Move to CPU
#Rescale result to match tomopy
rec_sirt = np.array(x_recon, dtype=np.complex64)
rec_sirt_final[slice_1] = np.array(rec_sirt.real, dtype=np.float32)
rec_sirt_final[slice_2] = np.array(rec_sirt.imag, dtype=np.float32)
return rec_sirt_final
obj = tomopy.shepp3d((num_slice, im_size, im_size)) # Generate an object.
#obj = tomopy.shepp3d(im_size) # Generate an object.
ang = tomopy.angles(num_angles) # Generate uniformly spaced tilt angles.
### Comparing to tomopy
sim = tomopy.project(obj, ang)
sino = {}
geom = {}
sino['Ns'] = 768 #3624#im_size*2 #Sinogram size after padding
sino['Ns_orig'] = im_size #size of original sinogram
sino['center'] = sino_center + (sino['Ns'] / 2 - sino['Ns_orig'] / 2
) #for padded sinogram
sino['angles'] = ang
params = init_nufft_params(sino, geom)
##Create a simulated object to test forward and back-projection routines
x = afnp.array(padmat(obj[slice_idx], np.array([sino['Ns'], sino['Ns']]), 0),
dtype=afnp.complex64)
t = time.time()
num_iter = 2
for i in range(1, num_iter + 1):
#Ax = (math.pi/2)*sino['Ns']*forward_project(x,params)
Ax = forward_project(x, params)
elapsed_time = (time.time() - t) / num_iter
print('Time for Forward Proj :', elapsed_time)
print('Min value of real FP=%f' % (Ax.real.min()))
print('Max value of real FP = %f' % (Ax.real.max()))
def gpuMBIR(tomo,angles,center,input_params):
"""
MBIR reconstruction using GPU based gridding operators
Inputs: tomo : 3D numpy sinogram array with dimensions same as tomopy
angles : Array of angles in radians
center : Floating point center of rotation
input_params : A dictionary with the keys
'gpu_device' : Device id of the gpu (For a 4 GPU cluster ; 0-3)
'oversamp_factor': A factor by which to pad the image/data for FFT
'num_iter' : Max number of MBIR iterations
'smoothness' : Regularization constant
'p': MRF shape param
"""
print('Starting GPU MBIR recon')
#allocate space for final answer
af.set_device(input_params['gpu_device']) #Set the device number for gpu based code
#Change tomopy format
new_tomo=np.transpose(tomo,(1,2,0)) #slice, columns, angles
im_size = new_tomo.shape[1]
num_slice = new_tomo.shape[0]
num_angles=new_tomo.shape[2]
pad_size=np.int16(im_size*input_params['oversamp_factor'])
# nufft_scaling = (np.pi/pad_size)**2
num_iter = input_params['num_iter']
mrf_sigma = input_params['smoothness']
mrf_p = input_params['p']
print('MRF params p=%f sigma=%f' %(mrf_p,mrf_sigma))
#Initialize structures for NUFFT
sino={}
geom={}
sino['Ns'] = pad_size#Sinogram size after padding
sino['Ns_orig'] = im_size #size of original sinogram
sino['center'] = center + (sino['Ns']/2 - sino['Ns_orig']/2) #for padded sinogram
sino['angles'] = angles
#Initialize NUFFT parameters
print('Initialize NUFFT params')
nufft_params = init_nufft_params(sino,geom)
temp_y = afnp.zeros((sino['Ns'],num_angles),dtype=afnp.complex64)
temp_x = afnp.zeros((sino['Ns'],sino['Ns']),dtype=afnp.complex64)
x_recon = afnp.zeros((num_slice/2,sino['Ns_orig'],sino['Ns_orig']),dtype=afnp.complex64)
pad_idx = slice(sino['Ns']/2-sino['Ns_orig']/2,sino['Ns']/2+sino['Ns_orig']/2)
#allocate output array
rec_mbir_final=np.zeros((num_slice,sino['Ns_orig'],sino['Ns_orig']),dtype=np.float32)
#Move all data to GPU
print('Moving data to GPU')
slice_1=slice(0,num_slice,2)
slice_2=slice(1,num_slice,2)
gdata=afnp.array(new_tomo[slice_1]+1j*new_tomo[slice_2],dtype=afnp.complex64)
gradient = afnp.zeros((num_slice/2,sino['Ns_orig'],sino['Ns_orig']), dtype=afnp.complex64)#temp array to store the derivative of cost func
z_recon = afnp.zeros((num_slice/2,sino['Ns_orig'],sino['Ns_orig']),dtype=afnp.complex64)#Nesterov method variables
t_nes = 1
#Compute Lipschitz of gradient
print('Computing Lipschitz of gradient')
x_ones= afnp.ones((1,sino['Ns_orig'],sino['Ns_orig']),dtype=afnp.complex64)
temp_x[pad_idx,pad_idx]=x_ones[0]
temp_proj=forward_project(temp_x,nufft_params)
temp_backproj=(back_project(temp_proj,nufft_params))[pad_idx,pad_idx]
print('Adding Hessian of regularizer')
temp_backproj2=afnp.zeros((1,sino['Ns_orig'],sino['Ns_orig']),dtype=afnp.complex64)
temp_backproj2[0]=temp_backproj
add_hessian(mrf_sigma,x_ones, temp_backproj2)
L = np.max([temp_backproj2.real.max(),temp_backproj2.imag.max()])
print('Lipschitz constant = %f' %(L))
del x_ones,temp_proj,temp_backproj,temp_backproj2
#loop over all slices
for iter_num in range(num_iter):
print('Iteration %d of %d'%(iter_num,num_iter))
#Derivative of the data fitting term
for i in range(num_slice/2):
temp_x[pad_idx,pad_idx]=x_recon[i]
Ax = forward_project(temp_x,nufft_params)
temp_y[pad_idx]=gdata[i]
gradient[i] =(back_project((Ax-temp_y),nufft_params))[pad_idx,pad_idx] #nufft_scaling
#Derivative of regularization term
tvd_update(mrf_p,mrf_sigma,x_recon, gradient)
#x_recon-=gradient/L
x_recon,z_recon,t_nes=nesterovOGM2update(x_recon,z_recon,t_nes,gradient,L)
#Move to CPU
#Rescale result to match tomopy
rec_mbir=np.array(x_recon,dtype=np.complex64)
rec_mbir_final[slice_1]=np.array(rec_mbir.real,dtype=np.float32)
rec_mbir_final[slice_2]=np.array(rec_mbir.imag,dtype=np.float32)
return rec_mbir_final