`corrct.operators`

Operators module.

@author: Nicola VIGANÒ, Computational Imaging group, CWI, The Netherlands, and ESRF - The European Synchrotron, Grenoble, France

Module Contents

Classes

`BaseTransform`	Base operator class.
`TransformFunctions`	Transform class that uses callables.
`ProjectorOperator`	Base projector class that fixes the projection interface.
`TransformIdentity`	Identity operator.
`TransformDiagonalScaling`	Diagonal scaling operator.
`TransformConvolution`	Convolution operator.
`BaseWaveletTransform`	Base Wavelet transform.
`TransformDecimatedWavelet`	Decimated wavelet Transform operator.
`TransformStationaryWavelet`	Stationary wavelet Transform operator.
`TransformGradient`	Gradient operator.
`TransformFourier`	Fourier transform operator.
`TransformLaplacian`	Laplacian transform operator.
`TransformSVD`	Singular value decomposition based decomposition operator.

Data

NDArrayInt

API

corrct.operators.NDArrayInt: None

class corrct.operators.BaseTransform[source]

Bases: scipy.sparse.linalg.LinearOperator, abc.ABC

Base operator class.

It implements the linear operator behavior that can be used with the solvers in the .solvers module, and by the solvers in scipy.sparse.linalg.

Parameters

dir_shape : NDArrayInt Shape of the direct space. adj_shape : NDArrayInt Shape of the adjoint space

Attributes

is_dir_operator : bool Flag indicating if the operator is a direct operator.

Notes

It assumes that the fields `dir_shape` and `adj_shape` have been set during the initialization of the derived classes.

Initialization

Initialize the base operator class.

dir_shape: corrct.operators.NDArrayInt: None

adj_shape: corrct.operators.NDArrayInt: None

_matvec(x: numpy.typing.NDArray) → numpy.typing.NDArray[source]

Implement the direct operator for column vectors from the right.

Parameters

x : NDArray Either row from the left or column from the right.

Returns

NDArray Result of applying the direct operator.

rmatvec(x: numpy.typing.NDArray) → numpy.typing.NDArray[source]

Implement the direct operator for row vectors from the left.

Parameters

x : NDArray Either row from the left or column from the right on transpose.

Returns

NDArray Result of applying the direct operator for row vectors.

_transpose() → corrct.operators.BaseTransform[source]

Create the transpose operator.

Returns

BaseTransform The transpose operator.

_adjoint() → corrct.operators.BaseTransform[source]

Create the adjoint operator.

Returns

BaseTransform The adjoint operator.

absolute() → corrct.operators.BaseTransform[source]

Return the absolute value of the operator.

Returns

BaseTransform The absolute value operator.

explicit() → numpy.typing.NDArray[source]

Return the explicit transformation matrix associated with the operator.

Returns

NDArray The explicit transformation matrix, as a NumPy array.

__call__(x: numpy.typing.NDArray) → numpy.typing.NDArray[source]

Apply the operator to the input vector x.

Parameters

x : NDArray Input vector.

Returns

result : NDArray The result of applying the operator to x.

abstract _op_direct(x: numpy.typing.NDArray) → numpy.typing.NDArray[source]

Apply the operator to the data.

Parameters

x : NDArray Data to process.

Returns

NDArray The processed data.

abstract _op_adjoint(x: numpy.typing.NDArray) → numpy.typing.NDArray[source]

Apply the adjoint operator to the data.

Parameters

x : NDArray Data to process.

Returns

NDArray The processed data.

class corrct.operators.TransformFunctions(dir_shape: Union[numpy.typing.ArrayLike, numpy.typing.NDArray], adj_shape: Union[numpy.typing.ArrayLike, numpy.typing.NDArray], A: Callable[[numpy.typing.NDArray], numpy.typing.NDArray], At: Optional[Callable[[numpy.typing.NDArray], numpy.typing.NDArray]] = None)[source]

Bases: corrct.operators.BaseTransform

Transform class that uses callables.

Initialization

Initialize the callable transform.

If the adjoint of the function is not given, the function is considered symmetric.

Parameters

dir_shape : ArrayLike Shape of the direct space. adj_shape : ArrayLike Shape of the adjoint space. A : Callable[[NDArray], NDArray] The transform function. At : Optional[Callable[[NDArray], NDArray]], optional The adjoint transform function, by default None

_op_direct(x: numpy.typing.NDArray) → numpy.typing.NDArray[source]

Apply the operator to the data.

Parameters

x : NDArray Data to process.

Returns

NDArray The processed data.

_op_adjoint(x: numpy.typing.NDArray) → numpy.typing.NDArray[source]

Apply the adjoint operator to the data.

Parameters

x : NDArray Data to process.

Returns

NDArray The processed data.

absolute() → corrct.operators.TransformFunctions[source]

Compute the absolute value of the operator. Raise an error, because not supported.

Raises

AttributeError Not supported operation.

class corrct.operators.ProjectorOperator[source]

Bases: corrct.operators.BaseTransform

Base projector class that fixes the projection interface.

Initialization

Initialize the base operator class.

property vol_shape: corrct.operators.NDArrayInt

Expose the direct space shape as volume shape.

Returns

NDArray The volume shape.

property prj_shape: corrct.operators.NDArrayInt

Expose the adjoint space shape as projection shape.

Returns

NDArray The projection shape.

abstract fp(x: numpy.typing.NDArray) → numpy.typing.NDArray[source]

Define the interface of the forward-projection.

Parameters

x : NDArray Input volume.

Returns

NDArray The projection data.

abstract bp(x: numpy.typing.NDArray) → numpy.typing.NDArray[source]

Define the interface for the back-projection.

Parameters

x : NDArray Input projection data.

Returns

NDArray The back-projected volume.

_op_direct(x: numpy.typing.NDArray) → numpy.typing.NDArray[source]

_op_adjoint(x: numpy.typing.NDArray) → numpy.typing.NDArray[source]

get_pre_weights() → Union[numpy.typing.NDArray, None][source]

Compute the pre-weights of the projector geometry (notably for cone-beam geometries).

Returns

Union[NDArray, None] The computed detector weights

class corrct.operators.TransformIdentity(x_shape: Union[numpy.typing.ArrayLike, numpy.typing.NDArray])[source]

Bases: corrct.operators.BaseTransform

Identity operator.

Initialization

Identity operator.

Parameters

x_shape : ArrayLike | NDArray Shape of the data.

_op_direct(x: numpy.typing.NDArray) → numpy.typing.NDArray[source]

_op_adjoint(x: numpy.typing.NDArray) → numpy.typing.NDArray[source]

class corrct.operators.TransformDiagonalScaling(x_shape: Union[numpy.typing.ArrayLike, numpy.typing.NDArray], scale: Union[numpy.typing.ArrayLike, numpy.typing.NDArray])[source]

Bases: corrct.operators.BaseTransform

Diagonal scaling operator.

Initialization

Diagonal scaling operator.

Parameters

x_shape : ArrayLike Shape of the data. scale : float or ArrayLike Operator diagonal.

scale: numpy.typing.NDArray: None

absolute() → corrct.operators.TransformDiagonalScaling[source]

Return the projection operator using the absolute value of the projection coefficients.

Returns

TransformDiagonalScaling The absolute value operator

_op_direct(x: numpy.typing.NDArray) → numpy.typing.NDArray[source]

_op_adjoint(x: numpy.typing.NDArray) → numpy.typing.NDArray[source]

class corrct.operators.TransformConvolution(x_shape: numpy.typing.ArrayLike, kernel: numpy.typing.ArrayLike, pad_mode: str = 'edge', is_symm: bool = True, flip_adjoint: bool = False)[source]

Bases: corrct.operators.BaseTransform

Convolution operator.

Parameters

x_shape : ArrayLike Shape of the direct space. kernel : ArrayLike The convolution kernel. pad_mode: str, optional The padding mode to use for the linear convolution. The default is “edge”. is_symm : bool, optional Whether the operator is symmetric or not. The default is True. flip_adjoint : bool, optional Whether the adjoint kernel should be flipped. The default is False. This is useful when the kernel is not symmetric.

Initialization

Initialize the base operator class.

kernel: numpy.typing.NDArray: None

pad_mode: str: None

is_symm: bool: None

flip_adjoint: bool: None

absolute() → corrct.operators.TransformConvolution[source]

Return the convolution operator using the absolute value of the kernel coefficients.

Returns

TransformConvolution The absolute value of the convolution operator.

_pad_valid(x: numpy.typing.NDArray) → tuple[numpy.typing.NDArray, numpy.typing.NDArray][source]

_crop_valid(x: numpy.typing.NDArray, pad_width: numpy.typing.NDArray) → numpy.typing.NDArray[source]

_op_direct(x: numpy.typing.NDArray) → numpy.typing.NDArray[source]

_op_adjoint(x: numpy.typing.NDArray) → numpy.typing.NDArray[source]

class corrct.operators.BaseWaveletTransform[source]

Bases: corrct.operators.BaseTransform, abc.ABC

Base Wavelet transform.

Initialization

Initialize the base operator class.

axes: corrct.operators.NDArrayInt: None

wavelet: str: None

labels: list[str]: None

_initialize_filter_bank() → None[source]

class corrct.operators.TransformDecimatedWavelet(x_shape: Union[numpy.typing.ArrayLike, numpy.typing.NDArray], wavelet: str, level: int, axes: Optional[numpy.typing.ArrayLike] = None, pad_on_demand: str = 'edge')[source]

Bases: corrct.operators.BaseWaveletTransform

Decimated wavelet Transform operator.

Initialization

Decimated wavelet Transform operator.

Parameters

x_shape : ArrayLike Shape of the data to be wavelet transformed. wavelet : str Wavelet type. level : int Number of wavelet decomposition levels. axes : int or tuple of int, optional Axes along which to do the transform. Defaults to None. pad_on_demand : str, optional Padding type to fit the 2 ** level shape requirements. Defaults to ‘edge’. Options are all the numpy.pad padding modes.

Raises

ValueError If the pywavelets package is not available or its version is not adequate.

direct_dwt(x: numpy.typing.NDArray) → list[source]

Perform the direct wavelet transform.

Parameters

x : NDArray Data to transform.

Returns

list Transformed data.

inverse_dwt(y: list) → numpy.typing.NDArray[source]

Perform the inverse wavelet transform.

Parameters

y : list Data to anti-transform.

Returns

NDArray Anti-transformed data.

_op_direct(x: numpy.typing.NDArray) → numpy.typing.NDArray[source]

_op_adjoint(y: numpy.typing.NDArray) → numpy.typing.NDArray[source]

class corrct.operators.TransformStationaryWavelet(x_shape: numpy.typing.ArrayLike, wavelet: str, level: int, axes: Optional[numpy.typing.ArrayLike] = None, pad_on_demand: str = 'edge', normalized: bool = True)[source]

Bases: corrct.operators.BaseWaveletTransform

Stationary wavelet Transform operator.

Initialization

Stationary wavelet Transform operator.

Parameters

x_shape : ArrayLike The shape of the data to be wavelet transformed. wavelet : str The type of wavelet to use. level : int Number of wavelet decomposition levels. axes : int or tuple of int, optional Axes along which to perform the transform. Default is None. pad_on_demand : str, optional The padding type to fit the 2 ** level shape requirements. Default is ‘constant’. Options are all the numpy.pad padding modes. normalized : bool, optional Whether to use a normalized transform. Default is True.

Raises

ValueError If the pywavelets package is not available or its version is not adequate.

direct_swt(x: numpy.typing.NDArray) → list[source]

Perform the direct wavelet transform.

Parameters

x : NDArray Data to transform.

Returns

list Transformed data.

inverse_swt(y: list) → numpy.typing.NDArray[source]

Perform the inverse wavelet transform.

Parameters

y : list Data to anti-transform.

Returns

NDArray Anti-transformed data.

_op_direct(x: numpy.typing.NDArray) → numpy.typing.NDArray[source]

_op_adjoint(y: numpy.typing.NDArray) → numpy.typing.NDArray[source]

class corrct.operators.TransformGradient(x_shape: numpy.typing.ArrayLike, axes: Optional[numpy.typing.ArrayLike] = None, pad_mode: str = 'edge')[source]

Bases: corrct.operators.BaseTransform

Gradient operator.

Parameters

x_shape : ArrayLike Shape of the data to be transformed. axes : Optional[ArrayLike], optional Axes along which to do the gradient. The default is None. pad_mode : str, optional Padding mode of the gradient. The default is “edge”.

Initialization

Initialize the base operator class.

gradient(x: numpy.typing.NDArray) → numpy.typing.NDArray[source]

Compute the gradient.

Parameters

x : NDArray Input data.

Returns

NDArray Gradient of data.

divergence(x: numpy.typing.NDArray) → numpy.typing.NDArray[source]

Compute the divergence - transpose of gradient.

Parameters

x : NDArray Input data.

Returns

NDArray Divergence of data.

_op_direct(x: numpy.typing.NDArray) → numpy.typing.NDArray[source]

_op_adjoint(y: numpy.typing.NDArray) → numpy.typing.NDArray[source]

class corrct.operators.TransformFourier(x_shape: numpy.typing.ArrayLike, axes: Optional[numpy.typing.ArrayLike] = None)[source]

Bases: corrct.operators.BaseTransform

Fourier transform operator.

Initialization

Fourier transform.

Parameters

x_shape : ArrayLike Shape of the data to be Fourier transformed. axes : Optional[ArrayLike], optional Axes along which to do the Fourier transform.

Returns

None

fft(x: numpy.typing.NDArray) → numpy.typing.NDArray[source]

Compute the fft.

Parameters

x : NDArray Input data.

Returns

NDArray FFT of data.

ifft(x: numpy.typing.NDArray) → numpy.typing.NDArray[source]

Compute the inverse of the fft.

Parameters

x : NDArray Input data.

Returns

NDArray iFFT of data.

_op_direct(x: numpy.typing.NDArray) → numpy.typing.NDArray[source]

_op_adjoint(y: numpy.typing.NDArray) → numpy.typing.NDArray[source]

class corrct.operators.TransformLaplacian(x_shape: numpy.typing.ArrayLike, axes: Optional[numpy.typing.ArrayLike] = None, pad_mode: str = 'edge')[source]

Bases: corrct.operators.BaseTransform

Laplacian transform operator.

Parameters

x_shape : ArrayLike Shape of the data to be transformed. axes : ArrayLike, optional Axes along which to do the Laplacian. The default is None. pad_mode : str, optional Padding mode of the Laplacian. The default is “edge”.

Initialization

Initialize the base operator class.

laplacian(x: numpy.typing.NDArray) → numpy.typing.NDArray[source]

Compute the laplacian.

Parameters

x : NDArray Input data.

Returns

NDArray Laplacian of the input data.

_op_direct(x: numpy.typing.NDArray) → numpy.typing.NDArray[source]

_op_adjoint(y: numpy.typing.NDArray) → numpy.typing.NDArray[source]

class corrct.operators.TransformSVD(x_shape, axes_rows=(0,), axes_cols=(-1,), rescale: bool = False)[source]

Bases: corrct.operators.BaseTransform

Singular value decomposition based decomposition operator.

Initialization

Singular value decomposition operator.

The SVD decomposition will be done over the flattened rows vs flatted cols. This means that the channels should always be the rows (expected to be only one dimension, usually), while the volume dimensions should always be the columns (expected to be the last two or three dimensions).

Parameters

x_shape : numpy.array_like Shape of the data to be wavelet transformed. axes_rows : tuple of int, optional Axes expanded in rows of the SVD. Defaults to (0, ). axes_cols : tuple of int, optional Axes expanded in cols of the SVD. Defaults to (-1, ).

Raises

IndexError In case the axes are outside the range.

U: Optional[numpy.typing.NDArray]: None

Vt: Optional[numpy.typing.NDArray]: None

direct_svd(x)[source]

Performs the SVD decomposition.

Parameters

x : numpy.array_like Data to transform.

Returns

tuple(U, s, Vt) Transformed data.

inverse_svd(U, s, Vt)[source]

Performs the inverse SVD decomposition.

Parameters

U : numpy.array_like Rows of the SVD decomposition. s : numpy.array_like Singular values. Vt : numpy.array_like Columns of the SVD decomposition.

Returns

numpy.array_like Anti-transformed data.

_op_direct(x)[source]

_op_adjoint(y)[source]

corrct.operators

Module Contents

Classes

Data

API

`corrct.operators`