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Reconstruction_pycuda.py
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import os
import sys
import numpy as np
import numpy.matlib
from scipy.interpolate import interp2d, griddata
import glob
import matplotlib.pyplot as plt
import pycuda.driver as drv
import pycuda.autoinit
from pycuda.compiler import SourceModule
import numpy.matlib
import pycuda.gpuarray
from math import ceil
import time
from GPUFuncs_pycuda import *
import logging
from scipy.signal import hilbert
from scipy.interpolate import RegularGridInterpolator
# define logger
logging.basicConfig(level=logging.INFO)
log = logging.getLogger(__name__)
# function alias starts
sin = np.sin
cos = np.cos
atan = np.arctan
tan = np.tan
sinc = np.sinc
sqrt = np.sqrt
repmat = numpy.matlib.repmat
# ceil = np.ceil
pi = np.pi
floor = np.floor
log2 = np.log2
fft = np.fft.fft
ifft = np.fft.ifft
fftshift = np.fft.fftshift
ifftshift = np.fft.ifftshift
real = np.real
# function alias ends
mod = DefineGPUFuns()
class ErrorDescription(object):
def __init__(self, value):
if (value == 1):
self.msg = 'Unknown variables'
elif (value == 2):
self.msg = 'Unknown data precision'
elif (value == 3):
self.msg = 'Number of file is different from number of projection data required'
elif (value == 4):
self.msg = 'Cutoff have to be pose between 0 and 0.5'
elif (value == 5):
self.msg = 'Smooth have to be pose between 0 and 1'
else:
self.msg = 'Unknown error'
def __str__(self):
return self.msg
class Reconstruction(object):
def __init__(self, params):
self.params = {'SourceInit': [0, 0, 0], 'DetectorInit': [0, 0, 0], 'StartAngle': 0, 'EndAngle': 0,
'NumberOfDetectorPixels': [0, 0], 'DetectorPixelSize': [0, 0], 'NumberOfViews': 0,
'ImagePixelSpacing': [0, 0, 0], 'NumberOfImage': [0, 0, 0], 'PhantomCenter': [0, 0, 0],
'RotationOrigin': [0, 0, 0], 'Method': 'Distance', 'FilterType': 'ram-lak',
'ReconCenter': [0, 0, 0], 'cutoff': 1, 'GPU': 0, 'DetectorShape': 'Flat', 'Pitch': 0,
'DetectorOffset': [0, 0]}
self.params = params
[self.nu, self.nv] = self.params['NumberOfDetectorPixels']
[self.du, self.dv] = self.params['DetectorPixelSize']
[self.nx, self.ny, self.nz] = self.params['NumberOfImage']
[self.dx, self.dy, self.dz] = self.params['ImagePixelSpacing']
self.Origin = np.array(self.params['RotationOrigin'])
self.PhantomCenter = np.array(self.params['PhantomCenter'])
self.cutoff = self.params['cutoff']
self.DetectorShape = self.params['DetectorShape']
self.P = self.params['Pitch']
self.Source = np.array(self.params['SourceInit'])
self.Detector = np.array(self.params['DetectorInit'])
self.SAD = np.sqrt(np.sum((self.Source - self.Origin) ** 2.0))
self.SDD = np.sqrt(np.sum((self.Source - self.Detector) ** 2.0))
self.HelicalTrans = self.P * (self.nv * self.dv) * self.SAD / self.SDD
self.nView = self.params['NumberOfViews']
self.sAngle = self.params['StartAngle']
self.eAngle = self.params['EndAngle']
self.Proj2pi = self.nView / ((self.eAngle - self.sAngle) / (2 * pi))
self.Method = self.params['Method']
self.FilterType = self.params['FilterType']
self.source_z0 = self.Source[2]
self.detector_z0 = self.Detector[2]
self.ReconCenter = self.params['ReconCenter']
self.DetectorOffset = self.params['DetectorOffset']
if self.params['GPU'] == 1:
self.GPU = True
else:
self.GPU = False
def LoadProj(self, filename, dtype=np.float32):
self.proj = np.fromfile(filename, dtype=dtype).reshape([self.nView, self.nv, self.nu])
def LoadRecon(self, filename, dtype=np.float32):
self.image = np.fromfile(filename, dtype=dtype).reshape([self.nz, self.ny, self.nx])
def SaveProj(self, filename):
self.proj.tofile(filename, sep='', format='')
def SaveRecon(self, filename):
self.image.tofile(filename, sep='', format='')
def Select_PI(self):
nu = self.nu
nv = self.nv
du = self.du
dv = -1 * self.dv
nx = self.nx
ny = self.ny
nz = self.nz
dx = self.dx
dy = -1 * self.dy
dz = -1 * self.dz
nViews = self.nView
R = self.SAD
D = self.SDD
sAngle = self.sAngle
eAngle = self.eAngle
angle = np.linspace(sAngle, eAngle, nViews + 1)
angle = angle[0:-1]
Source = self.Source
Detector = self.Detector
source_z0 = self.source_z0
detector_z0 = self.detector_z0
H = self.HelicalTrans
PhantomCenter = self.PhantomCenter
ReconCenter = self.ReconCenter
DetectorOffset = self.DetectorOffset
dtheta = angle[1] - angle[0]
angle_in = np.zeros([ny, nx], dtype=np.float32)
angle_out = np.zeros([ny, nx], dtype=np.float32)
weight = np.zeros([ny, nx], dtype=np.float32)
x = np.arange(-(nx - 1.0) / 2.0, (nx - 1.0) / 2.0 + 1) * dx
y = np.arange(-(ny - 1.0) / 2.0, (ny - 1.0) / 2.0 + 1) * dy
fov = np.sin(np.arctan((nu * du / 2) / D)) * R
for i in range(ny):
y1 = y[i]
r1 = np.arccos(y1 / R)
angle_in[i, :] = r1
angle_out[i, :] = -r1 + 2 * pi
x1 = -sqrt(fov ** 2 - y1 ** 2)
x2 = sqrt(fov ** 2 - y1 ** 2)
w1 = x - x1
w2 = x2 - x
w1[np.where(w1 < 0)] = 0
w2[np.where(w2 < 0)] = 0
weight[i, :] = np.sqrt(w1 * w2)
self.angle_in = angle_in
self.angle_out = angle_out
self.filtering_weight = weight
def DerivProj(self):
nu = self.nu
nv = self.nv
du = self.du
dv = -1 * self.dv
nx = self.nx
ny = self.ny
nz = self.nz
dx = self.dx
dy = -1 * self.dy
dz = -1 * self.dz
nViews = self.nView
R = self.SAD
D = self.SDD
sAngle = self.sAngle
eAngle = self.eAngle
angle = np.linspace(sAngle, eAngle, nViews + 1)
angle = angle[0:-1]
Source = self.Source
Detector = self.Detector
source_z0 = self.source_z0
detector_z0 = self.detector_z0
H = self.HelicalTrans
PhantomCenter = self.PhantomCenter
ReconCenter = self.ReconCenter
DetectorOffset = self.DetectorOffset
dtheta = angle[1] - angle[0]
u = np.arange(-(nu - 1.0) / 2.0, (nu - 1.0) / 2.0 + 1) * du
v = np.arange(-(nv - 1.0) / 2.0, (nv - 1.0) / 2.0 + 1) * dv
[uu, vv] = np.meshgrid(u, v)
A = np.sqrt(uu ** 2 + vv ** 2 + D ** 2)
# print(len(u), len(v))
self.proj_org = np.copy(self.proj)
proj0 = np.copy(self.proj)
proj1 = np.append(proj0, np.expand_dims(proj0[0, :, :], axis=0), axis=0)
dpdu = np.zeros(proj0.shape, dtype=np.float32)
proj0 = R * proj0 / A
dpdl = (proj1[1:, :, :] - proj1[:-1, :, :]) / dtheta
dpdu[:, :, :-1] = (proj0[:, :, 1:] - proj0[:, :, :-1]) / du
assert dpdl.shape == (nViews, nv, nu) and dpdu.shape == (nViews, nv, nu)
self.dpdu = dpdu
self.dpdl = dpdl
def CurvedDetectorConstruction(self, Source, DetectorCenter, SDD, angle):
eu = [cos(angle), sin(angle), 0]
ew = [sin(angle), -cos(angle), 0]
ev = [0, 0, 1]
self.da = self.du / self.SDD
u = (np.arange(0, self.nu) - (self.nu - 1) / 2.0) * self.da
v = (np.arange(0, self.nv) - (self.nv - 1) / 2.0) * self.dv
u += self.DetectorOffset[0]
v += self.DetectorOffset[1]
DetectorIndex = np.zeros([3, len(v), len(u)], dtype=np.float32)
U, V = np.meshgrid(u, v)
# V, U = np.meshgrid(v, u)
DetectorIndex[0, :, :] = Source[0] + SDD * sin(U) * eu[0] + SDD * cos(U) * ew[0] - V * ev[0]
DetectorIndex[1, :, :] = Source[1] + SDD * sin(U) * eu[1] + SDD * cos(U) * ew[1] - V * ev[1]
DetectorIndex[2, :, :] = Source[2] + SDD * sin(U) * eu[2] + SDD * cos(U) * ew[2] - V * ev[2]
u2 = (np.arange(0, self.nu + 1) - (self.nu - 1) / 2.0) * self.da - self.da / 2.0
v2 = (np.arange(0, self.nv + 1) - (self.nv - 1) / 2.0) * self.dv - self.dv / 2.0
u2 += self.DetectorOffset[0]
v2 += self.DetectorOffset[1]
DetectorBoundary = np.zeros([3, len(v2), len(u2)], dtype=np.float32)
U2, V2 = np.meshgrid(u2, v2)
DetectorBoundary[0, :, :] = Source[0] + SDD * sin(U2) * eu[0] + SDD * cos(U2) * ew[0] - V2 * ev[0]
DetectorBoundary[1, :, :] = Source[1] + SDD * sin(U2) * eu[1] + SDD * cos(U2) * ew[1] - V2 * ev[1]
DetectorBoundary[2, :, :] = Source[2] + SDD * sin(U2) * eu[2] + SDD * cos(U2) * ew[2] - V2 * ev[2]
return DetectorIndex, DetectorBoundary
def FlatDetectorConstruction(self, Source, DetectorCenter, SDD, angle):
tol_min = 1e-5
tol_max = 1e6
eu = [cos(angle), sin(angle), 0]
ew = [sin(angle), -cos(angle), 0]
ev = [0.0, 0.0, 1.0]
# [nu, nv] = self.params['NumberOfDetectorPixels']
# [du, dv] = self.params['DetectorPixelSize']
# [dx, dy, dz] = self.params['ImagePixelSpacing']
# [nx, ny, nz] = self.params['NumberOfImage']
# dv=-1.0*dv
u = (np.arange(0, self.nu) - (self.nu - 1.0) / 2.0) * self.du
v = (np.arange(0, self.nv) - (self.nv - 1.0) / 2.0) * self.dv
u += self.DetectorOffset[0]
v += self.DetectorOffset[1]
DetectorIndex = np.zeros([3, len(v), len(u)], dtype=np.float32)
U, V = np.meshgrid(u, v)
DetectorIndex[0, :, :] = Source[0] + U * eu[0] + SDD * ew[0] - V * ev[0]
DetectorIndex[1, :, :] = Source[1] + U * eu[1] + SDD * ew[1] - V * ev[1]
DetectorIndex[2, :, :] = Source[2] + U * eu[2] + SDD * ew[2] - V * ev[2]
u2 = (np.arange(0, self.nu + 1) - (self.nu - 1) / 2.0) * self.du - self.du / 2.0
v2 = (np.arange(0, self.nv + 1) - (self.nv - 1) / 2.0) * self.dv - self.dv / 2.0
u2 += self.DetectorOffset[0]
v2 += self.DetectorOffset[1]
DetectorBoundary = np.zeros([3, len(v2), len(u2)], dtype=np.float32)
U2, V2 = np.meshgrid(u2, v2)
DetectorBoundary[0, :, :] = Source[0] + U2 * eu[0] + SDD * ew[0] - V2 * ev[0]
DetectorBoundary[1, :, :] = Source[1] + U2 * eu[1] + SDD * ew[1] - V2 * ev[1]
DetectorBoundary[2, :, :] = Source[2] + U2 * eu[2] + SDD * ew[2] - V2 * ev[2]
return DetectorIndex, DetectorBoundary
@staticmethod
def _optimalGrid(GridSize):
if (sqrt(GridSize).is_integer()):
gridX = int(np.sqrt(GridSize))
gridY = gridX
else:
Candidates = np.arange(1, GridSize + 1)
Division = GridSize / Candidates
CheckInteger = Division % 1
Divisors = Candidates[np.where(CheckInteger == 0)]
DivisorIndex = int(len(Divisors) / 2)
gridX = Divisors[DivisorIndex]
gridY = Divisors[DivisorIndex - 1]
return (int(gridX), int(gridY))
@staticmethod
def Filter(N, pixel_size, FilterType, cutoff):
'''
TO DO: Ram-Lak filter implementation
Argument for name of filter
'''
try:
if cutoff > 1 or cutoff < 0:
raise ErrorDescription(4)
except ErrorDescription as e:
print(e)
x = np.arange(0, N) - (N - 1) / 2.0
h = np.zeros(len(x))
h[np.where(x == 0)] = 1 / (8 * pixel_size ** 2)
odds = np.where(x % 2.0 == 1)
h[odds] = -0.5 / (pi * pixel_size * x[odds]) ** 2
h = h[0:-1]
filter = abs(fftshift(fft(h)))
w = 2 * pi * x[0:-1] / (N - 1)
# print(filter.shape, w.shape)
if FilterType == 'ram-lak':
pass # Do nothing
elif FilterType == 'shepp-logan':
zero = np.where(w == 0)
tmp = filter[zero]
filter = filter * sin(w / (2.0 * cutoff)) / (w / (2.0 * cutoff))
filter[zero] = tmp * sin(w[zero] / (2.0 * cutoff))
elif FilterType == 'cosine':
filter = filter * cos(w / (2.0 * cutoff))
elif FilterType == 'hamming':
filter = filter * (0.54 + 0.46 * (cos(w / cutoff)))
elif FilterType == 'hann':
filter = filter * (0.5 + 0.5 * cos(w / cutoff))
filter[np.where(abs(w) > pi * cutoff / (2.0 * pixel_size))] = 0
return filter
def Filtering(self):
ki = (np.arange(0, self.nu + 1) - self.nu / 2.0) * self.du
p = (np.arange(0, self.nv + 1) - self.nv / 2.0) * self.dv
for i in range(self.proj.shape[0]):
self.proj[i, :, :] = self.filter_proj(self.proj[i, :, :], ki, p)
def filter_proj(self, proj, ki, p):
nu = self.nu
nv = self.nv
du = self.du
dv = -self.dv
ZeroPaddedLength = int(2 ** (ceil(log2(2.0 * (nu - 1)))))
R = self.SAD
D = self.SDD - R
[kk, pp] = np.meshgrid(ki[0:-1] * R / (R + D), p[0:-1] * R / (R + D))
weight = R / (sqrt(R ** 2.0 + kk ** 2.0 + pp ** 2.0))
deltaS = du * R / (R + D)
filter = Reconstruction.Filter(
ZeroPaddedLength + 1, du * R / (D + R), self.FilterType, self.cutoff)
weightd_proj = weight * proj
Q = np.zeros(weightd_proj.shape, dtype=np.float32)
for k in range(nv):
tmp = real(ifft(ifftshift(filter * fftshift(fft(weightd_proj[k, :], ZeroPaddedLength)))))
Q[k, :] = tmp[0:nu] * deltaS
return Q
def bpf_filter(self, N=4096):
nu = self.nu
nv = self.nv
du = self.du
dv = -1 * self.dv
nx = self.nx
ny = self.ny
nz = self.nz
dx = self.dx
dy = -1 * self.dy
dz = -1 * self.dz
nViews = self.nView
R = self.SAD
D = self.SDD
x = np.arange(-(nx - 1.0) / 2.0, (nx - 1.0) / 2.0 + 1) * dx
y = np.arange(-(ny - 1.0) / 2.0, (ny - 1.0) / 2.0 + 1) * dy
[xx, yy] = np.meshgrid(x, y)
fov = np.sin(np.arctan((nu * du / 2) / D)) * R
recon_filt = np.zeros(self.image.shape, dtype=np.float32)
fov_mask = np.zeros([ny, nx], dtype=np.float32)
fov_mask[np.sqrt(xx ** 2 + yy ** 2) <= fov] = 1
for i in range(nz):
for j in range(ny):
line = np.where(fov_mask[j, :] > 0)
# print(line, len(line[0]))
tmp = -np.imag(hilbert(self.image[i, j, line] * self.filtering_weight[j, line], N)) / (2 * pi)
# print(tmp.shape)
recon_filt[i, j, line] = tmp[0, :len(line[0])]
self.image = recon_filt
def bpf_constant(self):
nu = self.nu
nv = self.nv
du = self.du
dv = -1 * self.dv
nx = self.nx
ny = self.ny
nz = self.nz
dx = self.dx
dy = -1 * self.dy
dz = -1 * self.dz
nViews = self.nView
R = self.SAD
D = self.SDD
u = (np.arange(-(self.nu - 1.0) / 2.0, (self.nu - 1.0) / 2.0 + 1)) * du
v = (np.arange(-(self.nv - 1.0) / 2.0, (self.nv - 1.0) / 2.0 + 1)) * dv
assert len(u) == nu and len(v) == nv
u += self.DetectorOffset[0]
v += self.DetectorOffset[1]
sAngle = self.sAngle
eAngle = self.eAngle
angle = np.linspace(sAngle, eAngle, nViews + 1)
angle = angle[0:-1]
z = np.arange(-(nz - 1.0) / 2.0, (nz - 1.0) / 2.0 + 1) * dz
ev = np.array([0, 0, 1])
f = RegularGridInterpolator((angle, -v, u), np.flip(self.proj_org, axis=1), method='linear', bounds_error=False,
fill_value=0.0)
P0 = np.zeros([nz, ny, nx], dtype=np.float32)
for i in range(nz):
for j in range(ny):
angle1 = self.angle_in[j, 128]
angle2 = self.angle_out[j, 128]
r1 = np.array([-R * sin(angle1), R * cos(angle1), 0])
r2 = np.array([-R * sin(angle2), R * cos(angle2), 0])
eu1 = np.array([cos(angle1), sin(angle1), 0])
ew1 = np.array([sin(angle1), -cos(angle1), 0])
r0 = (r1 + r2) / 2 + ev * z[i]
u1 = D * np.dot(r0, eu1) / (R + np.dot(r0, ew1))
v1 = D * z[i] / (R + np.dot(r0, ew1))
# print(angle1, v1, u1, R, D)
p1 = f([angle1, v1, u1])
eu2 = np.array([cos(angle2), sin(angle2), 0])
ew2 = np.array([sin(angle2), -cos(angle2), 0])
r0 = (r1 + r2) / 2 + ev * z[i]
u2 = D * np.dot(r0, eu2) / (R + np.dot(r0, ew2))
v2 = D * z[i] / (R + np.dot(r0, ew2))
p2 = f([angle2, v2, u2])
P0[i, j, :] = (p1 + p2) / 2.0
self.P0 = P0
def angular_weight_calculator(self, angle_in, angle_out, dtheta, angle):
angular_weight = np.zeros(angle_in.shape, dtype=np.float32)
d_in = (angle - angle_in) / dtheta
d_out = (angle_out - angle) / dtheta
ind1 = np.where((angle - dtheta > angle_in) & (angle + dtheta < angle_out))
ind2 = np.where(angle + dtheta < angle_in)
ind3 = np.where(angle - dtheta > angle_out)
ind4 = np.where((angle + dtheta > angle_in) & (angle < angle_in))
ind5 = np.where((angle > angle_in) & (angle - dtheta < angle_in))
ind6 = np.where((angle + dtheta > angle_out) & (angle < angle_out))
ind7 = np.where((angle > angle_out) & (angle - dtheta < angle_out))
angular_weight[ind1] = 1.0
angular_weight[ind2] = 0.0
angular_weight[ind3] = 0.0
angular_weight[ind4] = ((1 + d_in[ind4]) ** 2) / 2.0
angular_weight[ind5] = 0.5 + d_in[ind5] - 0.5 * (d_in[ind5]) ** 2
angular_weight[ind6] = 0.5 + d_out[ind6] - 0.5 * (d_out[ind6]) ** 2
angular_weight[ind7] = ((1 + d_out[ind7]) ** 2) / 2.0
angular_weight2 = np.zeros([self.nz, self.ny, self.nx], dtype=np.float32)
for i in range(self.nz):
angular_weight2[i, :, :] = angular_weight
return angular_weight2
def backward_legacy(self):
nViews = self.params['NumberOfViews']
[nu, nv] = self.params['NumberOfDetectorPixels']
[du, dv] = self.params['DetectorPixelSize']
[dx, dy, dz] = self.params['ImagePixelSpacing']
[nx, ny, nz] = self.params['NumberOfImage']
cutoff = self.params['cutoff']
FilterType = self.params['FilterType']
dy = -1 * dy
dz = -1 * dz
dv = -1 * dv
Source_Init = np.array(self.params['SourceInit'])
Detector_Init = np.array(self.params['DetectorInit'])
StartAngle = self.params['StartAngle']
EndAngle = self.params['EndAngle']
Origin = np.array(self.params['Origin'])
PhantomCenter = np.array(self.params['PhantomCenter'])
gpu = self.params['GPU']
SAD = np.sqrt(np.sum((Source_Init - Origin) ** 2.0))
SDD = np.sqrt(np.sum((Source_Init - Detector_Init) ** 2.0))
# Calculates detector center
# angle = np.linspace(StartAngle, EndAngle, nViews + 1)
# angle = angle[0:-1]
# dtheta = angle[1] - angle[0]
# deltaS = du * SAD / SDD
# Xplane = (PhantomCenter[0] - nx / 2 + range(0, nx + 1)) * dx
# Yplane = (PhantomCenter[1] - ny / 2 + range(0, ny + 1)) * dy
# Zplane = (PhantomCenter[2] - nz / 2 + range(0, nz + 1)) * dz
# Xpixel = Xplane[0:-1]
# Ypixel = Yplane[0:-1]
# Zpixel = Zplane[0:-1]
# ki = (np.arange(0, nu + 1) - nu / 2.0) * du
# p = (np.arange(0, nv + 1) - nv / 2.0) * dv
alpha = 0
beta = 0
gamma = 0
eu = [cos(gamma) * cos(alpha), sin(alpha), sin(gamma)]
ev = [cos(gamma) * -sin(alpha), cos(gamma) * cos(alpha), sin(gamma)]
ew = [0, 0, 1]
# print('Variable initialization: ' + str(time.time() - start_time))
# Source = np.array([-SAD * sin(angle[0]), SAD * cos(angle[0]), 0]) # z-direction rotation
# Detector = np.array([(SDD - SAD) * sin(angle[0]), -(SDD - SAD) * cos(angle[0]), 0])
# DetectorLength = np.array(
# [np.arange(floor(-nu / 2), floor(nu / 2) + 1) * du, np.arange(floor(-nv / 2), floor(nv / 2) + 1) * dv])
# DetectorVectors = [eu, ev, ew]
# DetectorIndex = self.DetectorConstruction(Detector, DetectorLength, DetectorVectors, angle[0])
recon = np.zeros([nz, ny, nx], dtype=np.float32)
# plt.plot(ki)
# plt.show()
start_time = time.time()
if (self.params['Method'] == 'Distance'):
recon = self.distance_backproj()
elif (self.params['Method'] == 'Ray'):
pass
# recon = self.ray(DetectorIndex, Source, Detector, angle)
self.image = recon
def backward(self):
recon = np.zeros([self.nz, self.ny, self.nx], dtype=np.float32)
start_time = time.time()
if self.Method == 'Distance':
recon = self.distance_backproj()
elif self.Method == 'Ray':
pass
# recon = self.ray_backproj(DetectorIndex, Source, Detector, angle)
self.image = recon
def backward_bpf(self):
nu = self.nu
nv = self.nv
du = self.du
dv = -1 * self.dv
nx = self.nx
ny = self.ny
nz = self.nz
dx = self.dx
dy = -1 * self.dy
dz = -1 * self.dz
nViews = self.nView
R = self.SAD
D = self.SDD
sAngle = self.sAngle
eAngle = self.eAngle
angle = np.linspace(sAngle, eAngle, nViews + 1)
angle = angle[0:-1]
Source = self.Source
Detector = self.Detector
source_z0 = self.source_z0
detector_z0 = self.detector_z0
H = self.HelicalTrans
PhantomCenter = self.PhantomCenter
ReconCenter = self.ReconCenter
DetectorOffset = self.DetectorOffset
dtheta = angle[1] - angle[0]
Xpixel = ReconCenter[0] + (np.arange(0, nx) - (nx - 1) / 2.0) * dx
Ypixel = ReconCenter[1] + (np.arange(0, ny) - (ny - 1) / 2.0) * dy
Zpixel = ReconCenter[2] + (np.arange(0, nz) - (nz - 1) / 2.0) * dz
ki = (np.arange(0, nu + 1) - (nu - 1) / 2.0) * du
p = (np.arange(0, nv + 1) - (nv - 1) / 2.0) * dv
ki += DetectorOffset[0]
p += DetectorOffset[1]
recon = np.zeros([nz, ny, nx], dtype=np.float32)
if self.GPU:
device = drv.Device(0)
attrs = device.get_attributes()
MAX_THREAD_PER_BLOCK = attrs[pycuda._driver.device_attribute.MAX_THREADS_PER_BLOCK]
MAX_GRID_DIM_X = attrs[pycuda._driver.device_attribute.MAX_GRID_DIM_X]
TotalSize = nx * ny * nz
if (TotalSize < MAX_THREAD_PER_BLOCK):
blockX = nx * ny * nz
blockY = 1
blockZ = 1
gridX = 1
gridY = 1
else:
blockX = 16
blockY = 16
blockZ = 1
GridSize = ceil(TotalSize / (blockX * blockY))
try:
if (GridSize < MAX_GRID_DIM_X):
[gridX, gridY] = Reconstruction._optimalGrid(GridSize)
else:
raise ErrorDescription(6)
except ErrorDescription as e:
print(e)
sys.exit()
try:
if self.DetectorShape == 'Curved':
du = du / D
distance_backproj_arb = mod.get_function('curved_distance_backproj_arb')
elif self.DetectorShape == 'Flat':
# distance_backproj_arb = mod.get_function('flat_distance_backproj_arb')
# distance_backproj_arb = mod.get_function('flat_distance_backproj_arb2')
distance_backproj_arb = mod.get_function('flat_distance_backproj_arb_pi')
else:
raise ErrorDescription(1)
except ErrorDescription as e:
print(e)
sys.exit()
dest = pycuda.gpuarray.to_gpu(recon.flatten().astype(np.float32))
angular_weight_gpu = pycuda.gpuarray.to_gpu(recon.flatten().astype(np.float32))
x_pixel_gpu = pycuda.gpuarray.to_gpu(Xpixel.astype(np.float32))
y_pixel_gpu = pycuda.gpuarray.to_gpu(Ypixel.astype(np.float32))
z_pixel_gpu = pycuda.gpuarray.to_gpu(Zpixel.astype(np.float32))
u_plane_gpu = pycuda.gpuarray.to_gpu(ki.astype(np.float32))
v_plane_gpu = pycuda.gpuarray.to_gpu(p.astype(np.float32))
recon_param = np.array(
[dx, dy, dz, nx, ny, nz, nu, nv, du, dv, Source[0], Source[1], Source[2], Detector[0], Detector[1],
Detector[2], angle[0], 0.0, R, 0]).astype(np.float32)
recon_param_gpu = pycuda.gpuarray.zeros(20, np.float32)
# recon_param_gpu = drv.mem_alloc(recon_param.nbytes)
recon_param_gpu = pycuda.gpuarray.to_gpu(recon_param.flatten().astype(np.float32))
# Q = self.proj * dtheta
# Q_gpu = pycuda.gpuarray.to_gpu(Q.flatten().astype(np.float32))
for i in range(nViews):
log.debug(i)
Q1 = self.dpdu[i, :, :] * dtheta
Q1 = Q1.flatten().astype(np.float32)
Q2 = self.dpdl[i, :, :] * dtheta
Q2 = Q2.flatten().astype(np.float32)
Source[2] = source_z0 + H * angle[i] / (2 * pi)
Detector[2] = detector_z0 + H * angle[i] / (2 * pi)
angle1 = np.float32(angle[i])
angle2 = np.float32(0.0)
angular_weight = self.angular_weight_calculator(self.angle_in, self.angle_out, dtheta, angle1)
# angular_weight_gpu = pycuda.gpuarray.to_gpu(Q.flatten().astype(np.float32))
angular_weight_gpu.set(angular_weight.flatten().astype(np.float32))
recon_param = np.array(
[dx, dy, dz, nx, ny, nz, nu, nv, du, dv, Source[0], Source[1], Source[2], Detector[0], Detector[1],
Detector[2], angle[i], 0.0, R, D]).astype(np.float32)
recon_param_gpu.set(recon_param.flatten())
# print(blockX, blockY, blockZ, gridX, gridY)
distance_backproj_arb(dest, drv.In(Q1), drv.In(Q2), x_pixel_gpu, y_pixel_gpu, z_pixel_gpu, u_plane_gpu,
v_plane_gpu, angular_weight_gpu, recon_param_gpu, block=(blockX, blockY, blockZ),
grid=(gridX, gridY))
# pycuda.autoinit.context.synchronize()
del u_plane_gpu, v_plane_gpu, x_pixel_gpu, y_pixel_gpu, z_pixel_gpu, recon_param_gpu
recon = dest.get().reshape([nz, ny, nx]).astype(np.float32)
del dest
else:
for i in range(nViews):
Q = self.proj[i, :, :]
recon += self._distance_backproj_arb(Q, Xpixel, Ypixel, Zpixel, ki, p, angle[i], 0.0,
self.params) * dtheta
self.image = recon
def distance_backproj(self):
# proj should be filtered data
nu = self.nu
nv = self.nv
du = self.du
dv = -1 * self.dv
nx = self.nx
ny = self.ny
nz = self.nz
dx = self.dx
dy = -1 * self.dy
dz = -1 * self.dz
nViews = self.nView
R = self.SAD
D = self.SDD
sAngle = self.sAngle
eAngle = self.eAngle
angle = np.linspace(sAngle, eAngle, nViews + 1)
angle = angle[0:-1]
Source = self.Source
Detector = self.Detector
source_z0 = self.source_z0
detector_z0 = self.detector_z0
H = self.HelicalTrans
PhantomCenter = self.PhantomCenter
ReconCenter = self.ReconCenter
DetectorOffset = self.DetectorOffset
dtheta = angle[1] - angle[0]
Xpixel = ReconCenter[0] + (np.arange(0, nx) - (nx - 1) / 2.0) * dx
Ypixel = ReconCenter[1] + (np.arange(0, ny) - (ny - 1) / 2.0) * dy
Zpixel = ReconCenter[2] + (np.arange(0, nz) - (nz - 1) / 2.0) * dz
ki = (np.arange(0, nu + 1) - (nu - 1) / 2.0) * du
p = (np.arange(0, nv + 1) - (nv - 1) / 2.0) * dv
ki += DetectorOffset[0]
p += DetectorOffset[1]
recon = np.zeros([nz, ny, nx], dtype=np.float32)
if self.GPU:
device = drv.Device(0)
attrs = device.get_attributes()
MAX_THREAD_PER_BLOCK = attrs[pycuda._driver.device_attribute.MAX_THREADS_PER_BLOCK]
MAX_GRID_DIM_X = attrs[pycuda._driver.device_attribute.MAX_GRID_DIM_X]
TotalSize = nx * ny * nz
if (TotalSize < MAX_THREAD_PER_BLOCK):
blockX = nx * ny * nz
blockY = 1
blockZ = 1
gridX = 1
gridY = 1
else:
blockX = 32
blockY = 32
blockZ = 1
GridSize = ceil(TotalSize / (blockX * blockY))
try:
if (GridSize < MAX_GRID_DIM_X):
[gridX, gridY] = Reconstruction._optimalGrid(GridSize)
else:
raise ErrorDescription(6)
except ErrorDescription as e:
print(e)
sys.exit()
try:
if self.DetectorShape == 'Curved':
du = du / D
distance_backproj_arb = mod.get_function('curved_distance_backproj_arb')
elif self.DetectorShape == 'Flat':
# distance_backproj_arb = mod.get_function('flat_distance_backproj_arb')
distance_backproj_arb = mod.get_function('flat_distance_backproj_arb2')
else:
raise ErrorDescription(1)
except ErrorDescription as e:
print(e)
sys.exit()
dest = pycuda.gpuarray.to_gpu(recon.flatten().astype(np.float32))
x_pixel_gpu = pycuda.gpuarray.to_gpu(Xpixel.astype(np.float32))
y_pixel_gpu = pycuda.gpuarray.to_gpu(Ypixel.astype(np.float32))
z_pixel_gpu = pycuda.gpuarray.to_gpu(Zpixel.astype(np.float32))
u_plane_gpu = pycuda.gpuarray.to_gpu(ki.astype(np.float32))
v_plane_gpu = pycuda.gpuarray.to_gpu(p.astype(np.float32))
recon_param = np.array(
[dx, dy, dz, nx, ny, nz, nu, nv, du, dv, Source[0], Source[1], Source[2], Detector[0], Detector[1],
Detector[2], angle[0], 0.0, R, 0]).astype(np.float32)
recon_param_gpu = pycuda.gpuarray.zeros(20, np.float32)
# recon_param_gpu = drv.mem_alloc(recon_param.nbytes)
recon_param_gpu = pycuda.gpuarray.to_gpu(recon_param.flatten().astype(np.float32))
Q = self.proj * dtheta
Q_gpu = pycuda.gpuarray.to_gpu(Q.flatten().astype(np.float32))
for i in range(nViews):
log.debug(i)
# Q = self.proj[i, :, :] * dtheta
# Q = Q.flatten().astype(np.float32)
Source[2] = source_z0 + H * angle[i] / (2 * pi)
Detector[2] = detector_z0 + H * angle[i] / (2 * pi)
angle1 = np.float32(angle[i])
angle2 = np.float32(0.0)
recon_param = np.array(
[dx, dy, dz, nx, ny, nz, nu, nv, du, dv, Source[0], Source[1], Source[2], Detector[0], Detector[1],
Detector[2], angle[i], 0.0, R, i]).astype(np.float32)
recon_param_gpu.set(recon_param.flatten())
# drv.memcpy_htod(recon_param_gpu, recon_param)
distance_backproj_arb(dest, Q_gpu, x_pixel_gpu, y_pixel_gpu, z_pixel_gpu, u_plane_gpu, v_plane_gpu,
recon_param_gpu, block=(blockX, blockY, blockZ),
grid=(gridX, gridY))
# distance_backproj_arb(dest, Q_gpu, x_pixel_gpu, y_pixel_gpu, z_pixel_gpu, u_plane_gpu, v_plane_gpu,
# recon_param_gpu, Source[0], Source[1], Source[2], Detector[0], Detector[1],
# Detector[2], angle1, angle2, np.uint16(i), block=(blockX, blockY, blockZ),
# grid=(gridX, gridY))
# pycuda.autoinit.context.synchronize()
del u_plane_gpu, v_plane_gpu, x_pixel_gpu, y_pixel_gpu, z_pixel_gpu, recon_param_gpu
recon = dest.get().reshape([nz, ny, nx]).astype(np.float32)
del dest
else:
for i in range(nViews):
Q = self.proj[i, :, :]
recon += self._distance_backproj_arb(Q, Xpixel, Ypixel, Zpixel, ki, p, angle[i], 0.0,
self.params) * dtheta
return recon
@staticmethod
def _distance_backproj_arb(proj, Xpixel, Ypixel, Zpixel, Uplane, Vplane, angle1, angle2, params):
tol_min = 1e-6
[nu, nv] = params['NumberOfDetectorPixels']
[du, dv] = params['DetectorPixelSize']
[dx, dy, dz] = params['ImagePixelSpacing']
[nx, ny, nz] = params['NumberOfImage']
dx = -1 * dx
dy = -1 * dy
dv = -1 * dv
# angle1: rotation angle between point and X-axis
# angle2: rotation angle between point and XY-palne
Source = np.array(params['SourceInit'])
Detector = np.array(params['DetectorInit'])
R = sqrt(np.sum((np.array(Source) - np.array(params['PhantomCenter'])) ** 2.0))
recon_pixelsX = Xpixel
recon_pixelsY = Ypixel
recon_pixelsZ = Zpixel
recon = np.zeros([nz, ny, nx], dtype=np.float32)
f_angle = lambda x, y: atan(x / y) if y != 0 else atan(0) if x == 0 else -pi / 2 if x < 0 else pi / 2
fx = lambda x, y, z: x * cos(angle2) * cos(angle1) + y * cos(angle2) * sin(angle1) - z * sin(angle2) * cos(
angle1) * sin(f_angle(x, y)) - z * sin(angle2) * sin(angle1) * cos(f_angle(x, y))
fy = lambda x, y, z: y * cos(angle2) * cos(angle1) - x * cos(angle2) * sin(angle1) - z * sin(angle2) * cos(
angle1) * cos(f_angle(x, y)) + z * sin(angle2) * sin(angle1) * sin(f_angle(x, y))
fz = lambda x, y, z: z * cos(angle2) + sqrt(x ** 2 + y ** 2) * sin(angle2)
for i in range(nz):
for j in range(ny):
for k in range(nx):
# l = sqrt(recon_pixelsX[k] ** 2 + recon_pixelsY[j] ** 2 + recon_pixelsZ[i] ** 2)
xc = fx(recon_pixelsX[k], recon_pixelsY[j], recon_pixelsZ[i])
yc = fy(recon_pixelsX[k], recon_pixelsY[j], recon_pixelsZ[i])
zc = fz(recon_pixelsX[k], recon_pixelsY[j], recon_pixelsZ[i])
# yc = -(recon_pixelsX[k]) * sin(angle) + (recon_pixelsY[j]) * cos(angle)
x1 = fx((recon_pixelsX[k] - dx / 2), (recon_pixelsY[j] - dy / 2), recon_pixelsZ[i] - dz / 2)
y1 = fy((recon_pixelsX[k] - dx / 2), (recon_pixelsY[j] - dy / 2), recon_pixelsZ[i] - dz / 2)
z1 = fz((recon_pixelsX[k] - dx / 2), (recon_pixelsY[j] - dy / 2), recon_pixelsZ[i] - dz / 2)
x2 = fx((recon_pixelsX[k] + dx / 2), (recon_pixelsY[j] - dy / 2), recon_pixelsZ[i] - dz / 2)
y2 = fy((recon_pixelsX[k] + dx / 2), (recon_pixelsY[j] - dy / 2), recon_pixelsZ[i] - dz / 2)
z2 = fz((recon_pixelsX[k] + dx / 2), (recon_pixelsY[j] - dy / 2), recon_pixelsZ[i] - dz / 2)
x3 = fx((recon_pixelsX[k] + dx / 2), (recon_pixelsY[j] + dy / 2), recon_pixelsZ[i] - dz / 2)
y3 = fy((recon_pixelsX[k] + dx / 2), (recon_pixelsY[j] + dy / 2), recon_pixelsZ[i] - dz / 2)
z3 = fz((recon_pixelsX[k] + dx / 2), (recon_pixelsY[j] + dy / 2), recon_pixelsZ[i] - dz / 2)
x4 = fx((recon_pixelsX[k] - dx / 2), (recon_pixelsY[j] + dy / 2), recon_pixelsZ[i] - dz / 2)
y4 = fy((recon_pixelsX[k] - dx / 2), (recon_pixelsY[j] + dy / 2), recon_pixelsZ[i] - dz / 2)
z4 = fz((recon_pixelsX[k] - dx / 2), (recon_pixelsY[j] + dy / 2), recon_pixelsZ[i] - dz / 2)
x5 = fx((recon_pixelsX[k] - dx / 2), (recon_pixelsY[j] - dy / 2), recon_pixelsZ[i] + dz / 2)
y5 = fy((recon_pixelsX[k] - dx / 2), (recon_pixelsY[j] - dy / 2), recon_pixelsZ[i] + dz / 2)
z5 = fz((recon_pixelsX[k] - dx / 2), (recon_pixelsY[j] - dy / 2), recon_pixelsZ[i] + dz / 2)
x6 = fx((recon_pixelsX[k] + dx / 2), (recon_pixelsY[j] - dy / 2), recon_pixelsZ[i] + dz / 2)
y6 = fy((recon_pixelsX[k] + dx / 2), (recon_pixelsY[j] - dy / 2), recon_pixelsZ[i] + dz / 2)
z6 = fz((recon_pixelsX[k] + dx / 2), (recon_pixelsY[j] - dy / 2), recon_pixelsZ[i] + dz / 2)
x7 = fx((recon_pixelsX[k] + dx / 2), (recon_pixelsY[j] + dy / 2), recon_pixelsZ[i] + dz / 2)
y7 = fy((recon_pixelsX[k] + dx / 2), (recon_pixelsY[j] + dy / 2), recon_pixelsZ[i] + dz / 2)
z7 = fz((recon_pixelsX[k] + dx / 2), (recon_pixelsY[j] + dy / 2), recon_pixelsZ[i] + dz / 2)
x8 = fx((recon_pixelsX[k] - dx / 2), (recon_pixelsY[j] + dy / 2), recon_pixelsZ[i] + dz / 2)
y8 = fy((recon_pixelsX[k] - dx / 2), (recon_pixelsY[j] + dy / 2), recon_pixelsZ[i] + dz / 2)
z8 = fz((recon_pixelsX[k] - dx / 2), (recon_pixelsY[j] + dy / 2), recon_pixelsZ[i] + dz / 2)
slope_u1 = (Source[0] - x1) / (Source[1] - y1)
slope_u2 = (Source[0] - x2) / (Source[1] - y2)
slope_u3 = (Source[0] - x3) / (Source[1] - y3)
slope_u4 = (Source[0] - x4) / (Source[1] - y4)
slope_u5 = (Source[0] - x5) / (Source[1] - y5)
slope_u6 = (Source[0] - x6) / (Source[1] - y6)
slope_u7 = (Source[0] - x7) / (Source[1] - y7)
slope_u8 = (Source[0] - x8) / (Source[1] - y8)
slopes_u = [slope_u1, slope_u2, slope_u3, slope_u4, slope_u5, slope_u6, slope_u7, slope_u8]
slope_l = min(slopes_u)
slope_r = max(slopes_u)
coord_u1 = (slope_l * Detector[1]) + (Source[0] - slope_r * Source[1])
coord_u2 = (slope_r * Detector[1]) + (Source[0] - slope_r * Source[1])
u_l = floor((coord_u1 - Uplane[0]) / du)
u_r = floor((coord_u2 - Uplane[0]) / du)
s_index_u = int(min(u_l, u_r))
e_index_u = int(max(u_l, u_r))
slope_v1 = (Source[2] - z1) / (Source[1] - y1)
slope_v2 = (Source[2] - z2) / (Source[1] - y2)
slope_v3 = (Source[2] - z3) / (Source[1] - y3)
slope_v4 = (Source[2] - z4) / (Source[1] - y4)
slope_v5 = (Source[2] - z5) / (Source[1] - y5)
slope_v6 = (Source[2] - z6) / (Source[1] - y6)
slope_v7 = (Source[2] - z7) / (Source[1] - y7)
slope_v8 = (Source[2] - z8) / (Source[1] - y8)
slopes_v = [slope_v1, slope_v2, slope_v3, slope_v4, slope_v5, slope_v6, slope_v7, slope_v8]
slope_t = min(slopes_v)
slope_b = max(slopes_v)
coord_v1 = (slope_t * Detector[2]) + (Source[2] - slope_t * Source[1])
coord_v2 = (slope_b * Detector[2]) + (Source[2] - slope_b * Source[1])
v_l = floor((coord_v1 - Vplane[0]) / dv)
v_r = floor((coord_v2 - Vplane[0]) / dv)
s_index_v = int(min(v_l, v_r))
e_index_v = int(min(v_l, v_r))
for l in range(s_index_v, e_index_v + 1):
if (l < 0 or l > nu):
continue
if (s_index_v == e_index_v):
weight1 = 1.0
elif (l == s_index_v):
weight1 = (max(coord_v1, coord_v2) - Vplane[l + 1]) / abs(coord_v1 - coord_v2)
elif (l == e_index_v):
weight1 = (Vplane[l] - min(coord_v1, coord_v2)) / abs(coord_v1 - coord_v2)
else:
weight1 = abs(dv) / abs(coord_v1 - coord_v2)
for m in range(s_index_u, e_index_u + 1):
if (m < 0 or m > nv):
continue
if (s_index_u == e_index_u):
weight2 = 1.0
elif (m == s_index_u):
weight2 = (Uplane[k + 1] - min(coord_u1, coord_u2)) / abs(coord_u1 - coord_u2)
elif (m == e_index_u):
weight2 = (max(coord_u1, coord_u2) - Uplane[k]) / abs(coord_u1 - coord_u2)
else:
weight2 = abs(du) / abs(coord_u1 - coord_u2)
recon[i][j][k] += proj[l][m] * weight1 * weight2 * (R ** 2) / (R - yc) ** 2
return recon
@staticmethod
def _distance_backproj_about_z(proj, Xpixel, Ypixel, Zpixel, Uplane, Vplane, angle, params):
tol_min = 1e-6
[nu, nv] = params['NumberOfDetectorPixels']
[du, dv] = params['DetectorPixelSize']
[dx, dy, dz] = params['ImagePixelSpacing']
[nx, ny, nz] = params['NumberOfImage']
dx = -1 * dx
dy = -1 * dy
dv = -1 * dv
# SAD = params['SAD']
# SDD = parasm['SDD']
Source = np.array(params['SourceInit'])
Detector = np.array(params['DetectorInit'])
R = sqrt(np.sum((np.array(Source) - np.array(params['PhantomCenter'])) ** 2))
recon_pixelsX = Xpixel
recon_pixelsY = Ypixel
recon_pixelsZ = Zpixel
recon = np.zeros([nz, ny, nx], dtype=np.float32)
# recon_pixelsX = Xplane[0:-1] + dx / 2
# recon_pixelsY = Yplane[0:-1] + dy / 2
# recon_pixelsZ = Zplane[0:-1] + dz / 2
# [reconY, reconX] = np.meshgrid(recon_pixelsY, recon_pixlesZ)
# reconX_c1 = (reconX + dx / 2) * cos(angle) + (reconY + dy / 2) * sin(angle)
# reconX_c2 = (reconX - dx / 2) * cos(angle) + (reconY - dy / 2) * sin(angle)
# reconX_c3 = (reconX + dx / 2) * cos(angle) + (reconY - dy / 2) * sin(angle)
# reconX_c4 = (reconX - dx / 2) * cos(angle) + (reconY + dy / 2) * sin(angle)
#
# reconY_c1 = -(reconX + dx / 2) * sin(angle) + (reconY + dy / 2) * cos(angle)
# reconY_c2 = -(reconX - dx / 2) * sin(angle) + (reconY - dy / 2) * cos(angle)
# reconY_c3 = -(reconX + dx / 2) * sin(angle) + (reconY - dy / 2) * cos(angle)
# reconY_c4 = -(reconX - dx / 2) * sin(angle) + (reconY + dy / 2) * cos(angle)
#
# SlopeU_c1 = (Source[0] - reconX_c1) / (Source[1] - reconY_c1)
# SlopeU_c2 = (Source[0] - reconX_c2) / (Source[1] - reconY_c2)
# SlopeU_c3 = (Source[0] - reconX_c3) / (Source[1] - reconY_c3)
# SlopeU_c4 = (Source[0] - reconX_c4) / (Source[1] - reconY_c4)
# [reconZ, reconY] = np.meshgrid
for i in range(nz):
for j in range(ny):
for k in range(nx):
yc = -(recon_pixelsX[k]) * sin(angle) + (recon_pixelsY[j]) * cos(angle)
x1 = (recon_pixelsX[k] + dx / 2) * cos(angle) + (recon_pixelsY[j] + dy / 2) * sin(angle)
y1 = -(recon_pixelsX[k] + dx / 2) * sin(angle) + (recon_pixelsY[j] + dy / 2) * cos(angle)
slope1 = (Source[0] - x1) / (Source[1] - y1)
x2 = (recon_pixelsX[k] - dx / 2) * cos(angle) + (recon_pixelsY[j] - dy / 2) * sin(angle)
y2 = -(recon_pixelsX[k] - dx / 2) * sin(angle) + (recon_pixelsY[j] - dy / 2) * cos(angle)
slope2 = (Source[0] - x2) / (Source[1] - y2)
x3 = (recon_pixelsX[k] + dx / 2) * cos(angle) + (recon_pixelsY[j] - dy / 2) * sin(angle)
y3 = -(recon_pixelsX[k] + dx / 2) * sin(angle) + (recon_pixelsY[j] - dy / 2) * cos(angle)
slope3 = (Source[0] - x3) / (Source[1] - y3)
x4 = (recon_pixelsX[k] - dx / 2) * cos(angle) + (recon_pixelsY[j] + dy / 2) * sin(angle)
y4 = -(recon_pixelsX[k] - dx / 2) * sin(angle) + (recon_pixelsY[j] + dy / 2) * cos(angle)
slope4 = (Source[0] - x4) / (Source[1] - y4)
slopes_u = [slope1, slope2, slope3, slope4]
slope_l = min(slopes_u)
slope_r = max(slopes_u)
coord_u1 = (slope_l * Detector[1]) + (Source[0] - slope_r * Source[1])
coord_u2 = (slope_r * Detector[1]) + (Source[0] - slope_r * Source[1])
u_l = floor((coord_u1 - Uplane[0]) / du)
u_r = floor((coord_u2 - Uplane[0]) / du)
s_index_u = int(min(u_l, u_r))
e_index_u = int(max(u_l, u_r))
z1 = recon_pixelsZ[i] - dz / 2
z2 = recon_pixelsZ[i] + dz / 2
slopes_v = [(Source[2] - z1) / (Source[1] - yc), (Source[2] - z2) / (Source[1] - yc)]
slope_t = min(slopes_v)
slope_b = max(slopes_v)
coord_v1 = (slope_t * Detector[2]) + (Source[2] - slope_t * Source[1])
coord_v2 = (slope_b * Detector[2]) + (Source[2] - slope_b * Source[1])
v_l = floor((coord_v1 - Vplane[0]) / dv)
v_r = floor((coord_v2 - Vplane[0]) / dv)
s_index_v = int(min(v_l, v_r))
e_index_v = int(min(v_l, v_r))
for l in range(s_index_v, e_index_v + 1):
if (s_index_v == e_index_v):
weight1 = 1.0
elif (l == s_index_v):
weight1 = (max(coord_v1, coord_v2) - Vplane[l + 1]) / abs(coord_v1 - coord_v2)
elif (l == e_index_v):
weight1 = (Vplane[l] - min(coord_v1, coord_v2)) / abs(coord_v1 - coord_v2)
else:
weight1 = abs(dv) / abs(coord_v1 - coord_v2)
for m in range(s_index_u, e_index_u + 1):
if (s_index_u == e_index_u):
weight2 = 1.0
elif (m == s_index_u):
weight2 = (Uplane[k + 1] - min(coord_u1, coord_u2)) / abs(coord_u1 - coord_u2)
elif (m == e_index_u):
weight2 = (max(coord_u1, coord_u2) - Uplane[k]) / abs(coord_u1 - coord_u2)
else:
weight2 = abs(du) / abs(coord_u1 - coord_u2)
recon[i][j][k] += proj[l][m] * weight1 * weight2 * (R ** 2) / (R - yc) ** 2
return recon
def forward_legacy(self):
start_time = time.time()
nViews = self.params['NumberOfViews']
[nu, nv] = self.params['NumberOfDetectorPixels']
[du, dv] = self.params['DetectorPixelSize']
[dx, dy, dz] = self.params['ImagePixelSpacing']
[nx, ny, nz] = self.params['NumberOfImage']
dy = -1 * dy
dz = -1 * dz
Source_Init = np.array(self.params['SourceInit'])
Detector_Init = np.array(self.params['DetectorInit'])
StartAngle = self.params['StartAngle']
EndAngle = self.params['EndAngle']
Origin = np.array(self.params['Origin'])
PhantomCenter = np.array(self.params['PhantomCenter'])
HelicalPitch = self.params['Pitch']