def test_operator_norm_l2(self):
L2 = ops.L2Norm(image_size[0] * image_size[1], dtype=global_dtype, backend=global_backend)
# Check forward operator
assert np.sum(np.abs(L2 * yp.vec(self.x) - 0.5 * yp.norm(yp.vec(self.x)) ** 2)) < eps, '%f' % np.sum(np.abs(L2 * yp.vec(self.x) - 0.5 * yp.norm(yp.vec(self.x)) ** 2))
# Check gradient
L2.gradient_check()
def test_mechanical_operator_vector_sum(self):
''' Mechanical test of an operator-vector sum '''
# Test sum operations here
A_s = self.A + self.y
# Forward operator
assert np.sum(np.abs(A_s * yp.vec(self.x) - (self.A * yp.vec(self.x) + self.y))) < eps
# Adjoint
assert np.sum(np.abs(A_s.H(yp.vec(self.x)) - self.A.H(yp.vec(self.x)))) < eps
# Gradient Numerical Check
self.A.gradient_check()
def test_operator_matrix_multiply(self):
matrix_size = (10,10)
m = yp.rand(matrix_size, global_dtype, global_backend)
xm = yp.rand(matrix_size[1], global_dtype, global_backend)
M = ops.MatrixMultiply(m)
# Check Forward operator
assert yp.sumb(yp.abs(yp.vec(yp.changeBackend(M * xm, 'numpy')) - yp.vec(yp.changeBackend(m, 'numpy').dot(yp.changeBackend(xm, 'numpy'))))) < eps, "%f" % yp.sumb(yp.abs(yp.changeBackend(M * xm, 'numpy') - yp.changeBackend(m, 'numpy').dot(yp.changeBackend(xm, 'numpy'))[:, np.newaxis]))
# Check Adjoint
assert yp.sumb(yp.abs(yp.vec(yp.changeBackend(M.H * xm, 'numpy')) - yp.vec(np.conj(yp.changeBackend(m, 'numpy').T).dot(yp.changeBackend(xm, 'numpy'))))) < eps, "%f" % yp.sumb(yp.abs(yp.changeBackend(M.H * xm, 'numpy') - np.conj(yp.changeBackend(m, 'numpy').T).dot(yp.changeBackend(xm, 'numpy'))[:, np.newaxis]))
# Check gradient
M.gradient_check()
def test_mechanical_gradient_3(self):
''' Mechanical test for an inner linear operator with outer non-linear operator '''
L2 = ops.L2Norm(image_size[0] * image_size[1], dtype=global_dtype, backend=global_backend)
# Data difference function
Delta = (self.A - self.y)
# Objective Function
O = L2 * Delta
# Check forward operator
assert np.all(np.abs(O(yp.vec(self.x)) - 0.5 * np.sum(np.abs(Delta * yp.vec(self.x)) ** 2)) < eps)
# Check gradient operator (adjoint form)
O.gradient_check()
def test_operator_convolution_circular(self):
''' Circular Convolution Operator '''
# Generate circular convolution operator
C = ops.Convolution(self.h)
# Test forward operator
conv2 = lambda x, h: yp.changeBackend(np.fft.ifftshift((np.fft.ifft2(np.fft.fft2(x, axes=(0,1), norm='ortho') * np.fft.fft2(h, axes=(0,1), norm='ortho'), axes=(0,1), norm='ortho')), axes=(0,1)).astype(yp.getNativeDatatype(global_dtype, 'numpy')), global_backend)
x_np = yp.changeBackend(self.x, 'numpy')
h_np = yp.changeBackend(self.h, 'numpy')
assert np.sum(np.abs(yp.reshape(C * yp.vec(self.x), image_size) - conv2(x_np, h_np)) ** 2) < 1e-3, \
'SSE (%.4e) is greater than tolerance (%.4e)' % ((np.sum(np.abs((C * yp.vec(self.x)).reshape(image_size)-conv2(x,h)))), eps)
# Check gradient
C.gradient_check()
def test_operator_wavelet(self):
''' Wavelet Transform Operator '''
import pywt
wavelet_list = ['db1', 'haar', 'rbio1.1', 'bior1.1', 'bior4.4', 'sym12']
for wavelet_test in wavelet_list:
# Wavelet Transform
W = ops.WaveletTransform(image_size, wavelet_type=wavelet_test, use_cycle_spinning=False)
# Check forward operation
coeffs = pywt.wavedecn(self.x, wavelet=wavelet_test)
x_wavelet, coeff_slices = pywt.coeffs_to_array(coeffs)
assert yp.sumb(yp.abs(yp.changeBackend(W * self.x, 'numpy') - x_wavelet)) < eps, "Difference %.6e"
# Check inverse operation
coeffs_from_arr = pywt.array_to_coeffs(x_wavelet, coeff_slices)
cam_recon = pywt.waverecn(coeffs_from_arr, wavelet=wavelet_test)
assert yp.sumb(yp.abs(W.H * W * self.x - self.x)) < 1e-2
# Ensure that the wavelet transform isn't just identity (weird bug)
if W.shape[1] is yp.size(self.x):
assert yp.sumb(yp.abs(W * yp.vec(self.x) - yp.vec(self.x))) > 1e-2, "%s" % wavelet_test
def test_operator_stacking_nonlinear(self):
# Create list of operators
op_list_nonlinear = [
ops.FourierTransform(image_size),
ops.Identity(image_size),
ops.Exponential(image_size)
]
# Horizontally stacked operators
H_nl = ops.Hstack(op_list_nonlinear)
# Vertically stack x for forward operator
x3 = yp.changeBackend(np.vstack((self.x, self.x, self.x)), global_backend)
# Check forward operation
y2 = yp.zeros(op_list_nonlinear[0].shape[0], op_list_nonlinear[0].dtype, op_list_nonlinear[0].backend)
for op in op_list_nonlinear:
y2 = y2 + yp.vec(op * self.x)
assert yp.sumb(yp.abs(yp.vec(H_nl(x3)) - y2)) < eps, "%.4e" % yp.sumb(yp.abs(yp.vec(H_nl(x3)) - y2))
# Check gradient
H_nl.gradient_check()
# Create vertically stacked operator
V_nl = ops.Vstack(op_list_nonlinear)
# Check forward operator
y3 = np.empty((0,image_size[1]), dtype=yp.getNativeDatatype(global_dtype, 'numpy'))
for index, op in enumerate(op_list_nonlinear):
y3 = np.append(y3, (op * self.x), axis=0)
y3 = yp.changeBackend(y3, global_backend)
assert yp.sumb(yp.abs(V_nl * self.x - y3)) < eps, "%.4e" % yp.sumb(yp.abs(V_nl * self.x - y3))
# Check gradient
V_nl.gradient_check()
def test_mechanical_gradient_4(self):
''' Mechanical test for an outer non-linear operator with outer non-linear operator and a linear operator in-between'''
shift_true = np.asarray((-5,3)).astype(yp.getNativeDatatype(global_dtype, 'numpy'))
# Inner non-linear operator, linear operator in middle, and norm on outside
F = ops.FourierTransform(image_size, dtype=global_dtype, backend=global_backend)
D_object = ops.Diagonalize((F * yp.vec(self.x)).reshape(image_size), label='D_{object}', dtype=global_dtype, backend=global_backend)
R = ops.PhaseRamp(image_size, dtype=global_dtype, backend=global_backend)
A_shift = F.H * D_object * R
y = A_shift(shift_true)
L2 = ops.L2Norm(image_size[0] * image_size[1], dtype=global_dtype, backend=global_backend)
objective = L2 * (A_shift - self.y)
# Check gradient
objective.gradient_check()
def test_operator_norm_l1(self):
L1 = ops.L1Norm(image_size[0] * image_size[1], dtype=global_dtype)
# Forward operator
assert np.sum(np.abs(L1 * yp.vec(self.x) - np.sum(np.abs(yp.vec(self.x))))) < eps
def demosaic(frame,
order='grbg',
bayer_coupling_matrix=None,
debug=False,
white_balance=False):
# bayer_coupling_matrix = None
# bgrg: cells very green
# rggb: slight gteen tint
"""Demosaic a frame"""
frame_out = yp.zeros((int(yp.shape(frame)[0] / 2), int(yp.shape(frame)[1] / 2), 3), yp.getDatatype(frame), yp.getBackend(frame))
if bayer_coupling_matrix is not None:
frame_vec = yp.zeros((4, int(yp.shape(frame)[0] * yp.shape(frame)[1] / 4)), yp.getDatatype(frame), yp.getBackend(frame))
# Cast bayer coupling matrix
bayer_coupling_matrix = yp.cast(bayer_coupling_matrix,
yp.getDatatype(frame),
yp.getBackend(frame))
# Define frame vector
for bayer_pattern_index in range(4):
pixel_offsets = (0, 0)
if bayer_pattern_index == 3:
img_sub = frame[pixel_offsets[0]::2, pixel_offsets[1]::2]
elif bayer_pattern_index == 1:
img_sub = frame[pixel_offsets[0]::2, pixel_offsets[1] + 1::2]
elif bayer_pattern_index == 2:
img_sub = frame[pixel_offsets[0] + 1::2, pixel_offsets[1]::2]
elif bayer_pattern_index == 0:
img_sub = frame[pixel_offsets[0] + 1::2, pixel_offsets[1] + 1::2]
frame_vec[bayer_pattern_index, :] = yp.dcopy(yp.vec(img_sub))
if debug:
print("Channel %d mean is %g" % (bayer_pattern_index, yp.scalar(yp.real(yp.sum(img_sub)))))
# Perform demosaic using least squares
result = yp.linalg.lstsq(bayer_coupling_matrix, frame_vec)
result -= yp.amin(result)
result /= yp.amax(result)
for channel in range(3):
values = result[channel]
frame_out[:, :, channel] = yp.reshape(values, ((yp.shape(frame_out)[0], yp.shape(frame_out)[1])))
if white_balance:
frame_out[:, :, channel] -= yp.amin(frame_out[:, :, channel])
frame_out[:, :, channel] /= yp.amax(frame_out[:, :, channel])
return frame_out
else:
frame_out = yp.zeros((int(yp.shape(frame)[0] / 2), int(yp.shape(frame)[1] / 2), 3),
dtype=yp.getDatatype(frame), backend=yp.getBackend(frame))
# Get color order from order variable
b_index = order.find('b')
r_index = order.find('r')
g1_index = order.find('g')
# Get g2 from intersection of sets
g2_index = set(list(range(4))).difference({b_index, r_index, g1_index}).pop()
# +-----+-----+
# | 0 | 1 |
# +-----+-----|
# | 2 | 3 |
# +-----+-----|
if debug:
import matplotlib.pyplot as plt
plt.figure()
plt.imshow(frame[:12, :12])
r_start = (int(r_index in [2, 3]), int(r_index in [1, 3]))
g1_start = (int(g1_index in [2, 3]), int(g1_index in [1, 3]))
g2_start = (int(g2_index in [2, 3]), int(g2_index in [1, 3]))
b_start = (int(b_index in [2, 3]), int(b_index in [1, 3]))
frame_out[:, :, 0] = frame[r_start[0]::2, r_start[1]::2]
frame_out[:, :, 1] = (frame[g1_start[0]::2, g1_start[1]::2] + frame[g2_start[0]::2, g2_start[1]::2]) / 2.0
frame_out[:, :, 2] = frame[b_start[0]::2, b_start[1]::2]
# normalize
frame_out /= yp.max(frame_out)
# Perform white balancing if desired
if white_balance:
clims = []
for channel in range(3):
clims.append(yp.max(frame_out[:, :, channel]))
frame_out[:, :, channel] /= yp.max(frame_out[:, :, channel])
# Return frame
return frame_out