def tf_unmasked_op(x, idx=0):
scaling_norm = tf.dtypes.cast(
tf.math.sqrt(
tf.dtypes.cast(tf.math.reduce_prod(tf.shape(x)[1:3]), 'float32')),
x.dtype)
return tf.expand_dims(ifftshift(fft2d(fftshift(x[..., idx], axes=[1, 2])),
axes=[1, 2]),
axis=-1) / scaling_norm
def operator_and_matrix(self,
shape_info,
dtype,
use_placeholder,
ensure_self_adjoint_and_pd=False):
shape = shape_info.shape
# For this test class, we are creating Hermitian spectrums.
# We also want the spectrum to have eigenvalues bounded away from zero.
#
# pre_spectrum is bounded away from zero.
pre_spectrum = linear_operator_test_util.random_uniform(
shape=self._shape_to_spectrum_shape(shape),
dtype=dtype,
minval=1.,
maxval=2.)
pre_spectrum_c = _to_complex(pre_spectrum)
# Real{IFFT[pre_spectrum]}
# = IFFT[EvenPartOf[pre_spectrum]]
# is the IFFT of something that is also bounded away from zero.
# Therefore, FFT[pre_h] would be a well-conditioned spectrum.
pre_h = fft_ops.ifft2d(pre_spectrum_c)
# A spectrum is Hermitian iff it is the DFT of a real convolution kernel.
# So we will make spectrum = FFT[h], for real valued h.
h = math_ops.real(pre_h)
h_c = _to_complex(h)
spectrum = fft_ops.fft2d(h_c)
lin_op_spectrum = spectrum
if use_placeholder:
lin_op_spectrum = array_ops.placeholder_with_default(spectrum, shape=None)
operator = linalg.LinearOperatorCirculant2D(
lin_op_spectrum,
is_positive_definite=True if ensure_self_adjoint_and_pd else None,
is_self_adjoint=True if ensure_self_adjoint_and_pd else None,
input_output_dtype=dtype)
self.assertEqual(
operator.parameters,
{
"input_output_dtype": dtype,
"is_non_singular": None,
"is_positive_definite": (
True if ensure_self_adjoint_and_pd else None),
"is_self_adjoint": (
True if ensure_self_adjoint_and_pd else None),
"is_square": True,
"name": "LinearOperatorCirculant2D",
"spectrum": lin_op_spectrum,
})
mat = self._spectrum_to_circulant_2d(spectrum, shape, dtype=dtype)
return operator, mat
def ortho_fft2d(image):
image = _order_for_ft(image)
shift_axes = [2, 3]
scaling_norm = _compute_scaling_norm(image)
shifted_image = fftshift(image, axes=shift_axes)
kspace_shifted = fft2d(shifted_image)
kspace_unnormed = ifftshift(kspace_shifted, axes=shift_axes)
kspace = kspace_unnormed / scaling_norm
kspace = _order_after_ft(kspace)
return kspace
def operator_and_matrix(
self, shape_info, dtype, use_placeholder,
ensure_self_adjoint_and_pd=False):
shape = shape_info.shape
# For this test class, we are creating Hermitian spectrums.
# We also want the spectrum to have eigenvalues bounded away from zero.
#
# pre_spectrum is bounded away from zero.
pre_spectrum = linear_operator_test_util.random_uniform(
shape=self._shape_to_spectrum_shape(shape),
dtype=dtype,
minval=1.,
maxval=2.)
pre_spectrum_c = _to_complex(pre_spectrum)
# Real{IFFT[pre_spectrum]}
# = IFFT[EvenPartOf[pre_spectrum]]
# is the IFFT of something that is also bounded away from zero.
# Therefore, FFT[pre_h] would be a well-conditioned spectrum.
pre_h = fft_ops.ifft2d(pre_spectrum_c)
# A spectrum is Hermitian iff it is the DFT of a real convolution kernel.
# So we will make spectrum = FFT[h], for real valued h.
h = math_ops.real(pre_h)
h_c = _to_complex(h)
spectrum = fft_ops.fft2d(h_c)
lin_op_spectrum = spectrum
if use_placeholder:
lin_op_spectrum = array_ops.placeholder_with_default(spectrum, shape=None)
operator = linalg.LinearOperatorCirculant2D(
lin_op_spectrum,
is_positive_definite=True if ensure_self_adjoint_and_pd else None,
is_self_adjoint=True if ensure_self_adjoint_and_pd else None,
input_output_dtype=dtype)
mat = self._spectrum_to_circulant_2d(spectrum, shape, dtype=dtype)
return operator, mat
def op(self, inputs):
if self.multicoil:
if self.masked:
image, mask, smaps = inputs
else:
image, smaps = inputs
else:
if self.masked:
image, mask = inputs
else:
image = inputs
image = image[..., 0]
scaling_norm = _compute_scaling_norm(image)
if self.multicoil:
image = tf.expand_dims(image, axis=1)
image = image * smaps
shifted_image = fftshift(image, axes=self.shift_axes)
kspace_shifted = fft2d(shifted_image)
kspace_unnormed = ifftshift(kspace_shifted, axes=self.shift_axes)
kspace = kspace_unnormed[..., None] / scaling_norm
if self.masked:
kspace = _mask_tf([kspace, mask])
return kspace
def _spectrum_to_circulant_2d(self, spectrum, shape, dtype):
"""Creates a block circulant matrix from a spectrum.
Intentionally done in an explicit yet inefficient way. This provides a
cross check to the main code that uses fancy reshapes.
Args:
spectrum: Float or complex `Tensor`.
shape: Python list. Desired shape of returned matrix.
dtype: Type to cast the returned matrix to.
Returns:
Block circulant (batch) matrix of desired `dtype`.
"""
spectrum = _to_complex(spectrum)
spectrum_shape = self._shape_to_spectrum_shape(shape)
domain_dimension = spectrum_shape[-1]
if not domain_dimension:
return array_ops.zeros(shape, dtype)
block_shape = spectrum_shape[-2:]
# Explicitly compute the action of spectrum on basis vectors.
matrix_rows = []
for n0 in range(block_shape[0]):
for n1 in range(block_shape[1]):
x = np.zeros(block_shape)
# x is a basis vector.
x[n0, n1] = 1.0
fft_x = fft_ops.fft2d(math_ops.cast(x, spectrum.dtype))
h_convolve_x = fft_ops.ifft2d(spectrum * fft_x)
# We want the flat version of the action of the operator on a basis
# vector, not the block version.
h_convolve_x = array_ops.reshape(h_convolve_x, shape[:-1])
matrix_rows.append(h_convolve_x)
matrix = array_ops.stack(matrix_rows, axis=-1)
return math_ops.cast(matrix, dtype)
def _spectrum_to_circulant_2d(self, spectrum, shape, dtype):
"""Creates a block circulant matrix from a spectrum.
Intentionally done in an explicit yet inefficient way. This provides a
cross check to the main code that uses fancy reshapes.
Args:
spectrum: Float or complex `Tensor`.
shape: Python list. Desired shape of returned matrix.
dtype: Type to cast the returned matrix to.
Returns:
Block circulant (batch) matrix of desired `dtype`.
"""
spectrum = _to_complex(spectrum)
spectrum_shape = self._shape_to_spectrum_shape(shape)
domain_dimension = spectrum_shape[-1]
if not domain_dimension:
return array_ops.zeros(shape, dtype)
block_shape = spectrum_shape[-2:]
# Explicitly compute the action of spectrum on basis vectors.
matrix_rows = []
for n0 in range(block_shape[0]):
for n1 in range(block_shape[1]):
x = np.zeros(block_shape)
# x is a basis vector.
x[n0, n1] = 1.0
fft_x = fft_ops.fft2d(x.astype(np.complex64))
h_convolve_x = fft_ops.ifft2d(spectrum * fft_x)
# We want the flat version of the action of the operator on a basis
# vector, not the block version.
h_convolve_x = array_ops.reshape(h_convolve_x, shape[:-1])
matrix_rows.append(h_convolve_x)
matrix = array_ops.stack(matrix_rows, axis=-1)
return math_ops.cast(matrix, dtype)
