Projectors

mumott provides four different implementations of projectors suitable for SAXS tomography. While they should yield approximately equivalent results, they differ with respect to the resources they require.

SAXSProjectorCUDA and SAXSProjectorBilinear implement an equivalent algorithm for GPU and CPU resources, respectively. These two options are recommended in terms of speed and ease of use.

SAXSProjectorAstra provides an interface to a GPU implementation in the ASTRA toolbox. Finally, SAXSProjectorNumba provides a CPU implementation using the numba library.

class mumott.methods.projectors.SAXSProjectorBilinear(geometry)[source]

Projector for transforms of tensor fields from three-dimensional space to projection space using a bilinear interpolation algorithm that produces results similar to those of SAXSProjectorCUDA using CPU computation.

Parameters

geometry (Geometry) – An instance of Geometry containing the necessary vectors to compute forwared and adjoint projections.

adjoint(projections, indices=None)[source]

Compute the adjoint of a set of projections according to the system geometry.

Parameters

  • projections (ndarray[Any, dtype[TypeVar(_ScalarType_co, bound= generic, covariant=True)]]) – An array containing coefficients in its last dimension, from e.g. the residual of measured data and forward projections. The first dimension should match indices in size, and the second and third dimensions should match the system projection geometry. The array must be contiguous and row-major.

  • indices (Optional[ndarray[Any, dtype[int]]]) – A one-dimensional array containing one or more indices indicating from which projections the adjoint is to be computed.

Return type

ndarray[Any, dtype[TypeVar(_ScalarType_co, bound= generic, covariant=True)]]

Returns

The adjoint of the provided projections. An array with four dimensions (X, Y, Z, P), where the first three dimensions are spatial and the last dimension runs over coefficients.

property dtype: Union[dtype[Any], None, type[Any], _SupportsDType[dtype[Any]], str, tuple[Any, int], tuple[Any, Union[SupportsIndex, collections.abc.Sequence[SupportsIndex]]], list[Any], _DTypeDict, tuple[Any, Any]]

Preferred dtype of this Projector.

forward(field, indices=None)[source]

Compute the forward projection of a tensor field.

Parameters

  • field (ndarray[Any, dtype[TypeVar(_ScalarType_co, bound= generic, covariant=True)]]) – An array containing coefficients in its fourth dimension, which are to be projected into two dimensions. The first three dimensions should match the volume_shape of the sample.

  • indices (Optional[ndarray[Any, dtype[int]]]) – A one-dimensional array containing one or more indices indicating which projections are to be computed. If None, all projections will be computed.

Return type

ndarray[Any, dtype[TypeVar(_ScalarType_co, bound= generic, covariant=True)]]

Returns

An array with four dimensions (I, J, K, L), where the first dimension matches indices, such that projection[i] corresponds to the geometry of projection indices[i]. The second and third dimension contain the pixels in the J and K dimension respectively, whereas the last dimension is the coefficient dimension, matching field[-1].

property is_dirty: bool

Returns True if the system geometry has changed without the projection geometry having been updated.

property number_of_projections: int

The number of projections as defined by the length of the Geometry object attached to this instance.

property projection_shape: Tuple[int]

The shape of each projection defined by the Geometry object attached to this instance, as a tuple.

property volume_shape: Tuple[int]

The shape of the volume defined by the Geometry object attached to this instance, as a tuple.

class mumott.methods.projectors.SAXSProjectorCUDA(geometry)[source]

Projector for transforms of tensor fields from three-dimensional space to projection space. Uses a projection algorithm implemented in numba.cuda.

Parameters

geometry (Geometry) – An instance of Geometry containing the necessary vectors to compute forwared and adjoint projections.

adjoint(projections, indices=None)

Compute the adjoint of a set of projections according to the system geometry.

Parameters

  • projections (ndarray[Any, dtype[TypeVar(_ScalarType_co, bound= generic, covariant=True)]]) – An array containing coefficients in its last dimension, from e.g. the residual of measured data and forward projections. The first dimension should match indices in size, and the second and third dimensions should match the system projection geometry. The array must be contiguous and row-major.

  • indices (Optional[ndarray[Any, dtype[int]]]) – A one-dimensional array containing one or more indices indicating from which projections the adjoint is to be computed.

Return type

ndarray[Any, dtype[TypeVar(_ScalarType_co, bound= generic, covariant=True)]]

Returns

The adjoint of the provided projections. An array with four dimensions (X, Y, Z, P), where the first three dimensions are spatial and the last dimension runs over coefficients.

property dtype: Union[dtype[Any], None, type[Any], _SupportsDType[dtype[Any]], str, tuple[Any, int], tuple[Any, Union[SupportsIndex, collections.abc.Sequence[SupportsIndex]]], list[Any], _DTypeDict, tuple[Any, Any]]

Preferred dtype of this Projector.

forward(field, indices=None)

Compute the forward projection of a tensor field.

Parameters

  • field (ndarray[Any, dtype[TypeVar(_ScalarType_co, bound= generic, covariant=True)]]) – An array containing coefficients in its fourth dimension, which are to be projected into two dimensions. The first three dimensions should match the volume_shape of the sample.

  • indices (Optional[ndarray[Any, dtype[int]]]) – A one-dimensional array containing one or more indices indicating which projections are to be computed. If None, all projections will be computed.

Return type

ndarray[Any, dtype[TypeVar(_ScalarType_co, bound= generic, covariant=True)]]

Returns

An array with four dimensions (I, J, K, L), where the first dimension matches indices, such that projection[i] corresponds to the geometry of projection indices[i]. The second and third dimension contain the pixels in the J and K dimension respectively, whereas the last dimension is the coefficient dimension, matching field[-1].

property is_dirty: bool

Returns True if the system geometry has changed without the projection geometry having been updated.

property number_of_projections: int

The number of projections as defined by the length of the Geometry object attached to this instance.

property projection_shape: Tuple[int]

The shape of each projection defined by the Geometry object attached to this instance, as a tuple.

property volume_shape: Tuple[int]

The shape of the volume defined by the Geometry object attached to this instance, as a tuple.

class mumott.methods.projectors.SAXSProjectorAstra(*args, **kwargs)[source]

Projector for transforms of tensor fields from three-dimensional space to projection space.

This class provides wrappers for interoperability with the python bindings for ASTRA, a tomography toolbox which implements GPU-based computations for tomography.

Parameters

geometry (Geometry) – An instance of Geometry containing the necessary vectors to compute forwared and adjoint projections.

adjoint(projections, indices=None)[source]

Compute the adjoint of a set of projections according to the system geometry.

Parameters

  • projections (ndarray[Any, dtype[TypeVar(_ScalarType_co, bound= generic, covariant=True)]]) – An array containing coefficients in its last dimension, from e.g. the residual of measured data and forward projections. The first dimension should match indices in size, and the second and third dimensions should match the system projection geometry.

  • indices (Optional[ndarray[Any, dtype[int]]]) – A one-dimensional array containing one or more indices indicating from which projections the adjoint is to be computed.

Return type

ndarray[Any, dtype[TypeVar(_ScalarType_co, bound= generic, covariant=True)]]

Returns

The adjoint of the provided projections. An array with four dimensions (X, Y, Z, P), where the first three dimensions are spatial and the last dimension runs over coefficients.

property dtype: Union[dtype[Any], None, type[Any], _SupportsDType[dtype[Any]], str, tuple[Any, int], tuple[Any, Union[SupportsIndex, collections.abc.Sequence[SupportsIndex]]], list[Any], _DTypeDict, tuple[Any, Any]]

The dtype input fields and projections require.

forward(field, indices=None)[source]

Compute the forward projection of a tensor field.

Parameters

  • field (ndarray[Any, dtype[TypeVar(_ScalarType_co, bound= generic, covariant=True)]]) – An array containing coefficients in its fourth dimension, which are to be projected into two dimensions. The first three dimensions should match the volume_shape of the sample.

  • indices (Optional[ndarray[Any, dtype[int]]]) – Must be None since the computation of individual projections is not supported for this projector.

Return type

ndarray[Any, dtype[TypeVar(_ScalarType_co, bound= generic, covariant=True)]]

Returns

An array with four dimensions (I, J, K, L), where the first dimension corresponds to projection index. The second and third dimension contain the pixels in the J and K dimension respectively, whereas the last dimension is the coefficient dimension, matching field[-1].

property is_dirty: bool

Returns True if the system geometry has changed without the projection geometry having been updated.

property number_of_projections: int

The number of projections as defined by the length of the Geometry object attached to this instance.

property projection_shape: Tuple[int]

The shape of each projection defined by the Geometry object attached to this instance, as a tuple.

property volume_shape: Tuple[int]

The shape of the volume defined by the Geometry object attached to this instance, as a tuple.

class mumott.methods.projectors.SAXSProjectorNumba(*args, **kwargs)[source]

Projector for transforms of tensor fields from three-dimensional space to projection space.

Parameters

  • geometry (Geometry) – An instance of Geometry containing the necessary vectors to compute forwared and adjoint projections.

  • step_size (np.float64) – A number 0 < step_size <= 1 that indicates the degree of upsampling when computing projections. Default is 0.5.

adjoint(projections, indices=None)[source]

Compute the adjoint of a set of projections according to the system geometry.

Parameters

  • projections (ndarray[Any, dtype[TypeVar(_ScalarType_co, bound= generic, covariant=True)]]) – An array containing coefficients in its last dimension, from e.g. the residual of measured data and forward projections. The first dimension should match indices in size, and the second and third dimensions should match the system projection geometry.

  • indices (Optional[ndarray[Any, dtype[int]]]) – A one-dimensional array containing one or more indices indicating from which projections the adjoint is to be computed.

Return type

ndarray[Any, dtype[TypeVar(_ScalarType_co, bound= generic, covariant=True)]]

Returns

The adjoint of the provided projections. An array with four dimensions (X, Y, Z, P), where the first three dimensions are spatial and the last dimension runs over coefficients.

create_sampling_kernel(kernel_dimensions=(3, 3), kernel_width=(1.0, 1.0), kernel_type='bessel')[source]

Creates a kernel to emulate the point spread function (PSF) of the beam. This can improve the accuracy of the projection function.

Parameters

  • kernel_dimensions (Tuple[int, int]) – A tuple of how many points should be sampled in each direction of the kernel. The total number of line integrals per pixel in the data is kernel_dimensions[0] * kernel_dimensions[1].

  • kernel_width (Tuple[float, float]) – Width parameter for the kernel in units of pixels. Typically the full-width-half-maximum (FWHM) of the beam used for data acquisition.

  • kernel_type (str) –

    The type of kernel to use. Acceptable values are 'bessel', 'rectangular', and 'gaussian'.

    'bessel' uses a sinc function multiplied by a Lanczos window with the width parameter being the first Bessel zero. This gives a sharply peaked distribution that goes to zero at twice the full width half maximum, and samples are taken up to this zero.

    'rectangular' samples uniformly in a rectangle of size kernel_width.

    'gaussian' uses a normal distribution with the FWHM given by kernel_width sampled up to twice the FWHM.

Return type

None

property dtype: Union[dtype[Any], None, type[Any], _SupportsDType[dtype[Any]], str, tuple[Any, int], tuple[Any, Union[SupportsIndex, collections.abc.Sequence[SupportsIndex]]], list[Any], _DTypeDict, tuple[Any, Any]]

Preferred dtype of this Projector.

forward(field, indices=None)[source]

Compute the forward projection of a tensor field.

Parameters

  • field (ndarray[Any, dtype[TypeVar(_ScalarType_co, bound= generic, covariant=True)]]) – An array containing coefficients in its fourth dimension, which are to be projected into two dimensions. The first three dimensions should match the volume_shape of the sample.

  • indices (Optional[ndarray[Any, dtype[int]]]) – A one-dimensional array containing one or more indices indicating which projections are to be computed. If None, all projections will be computed.

Return type

ndarray[Any, dtype[TypeVar(_ScalarType_co, bound= generic, covariant=True)]]

Returns

An array with four dimensions (I, J, K, L), where the first dimension matches indices, such that projection[i] corresponds to the geometry of projection indices[i]. The second and third dimension contain the pixels in the J and K dimension respectively, whereas the last dimension is the coefficient dimension, matching field[-1].

property is_dirty: bool

Returns True if the system geometry has changed without the projection geometry having been updated.

property kernel_offsets: ndarray[Any, dtype[float64]]

Offsets for the sampling profile kernel.

property number_of_projections: int

The number of projections as defined by the length of the Geometry object attached to this instance.

property projection_shape: Tuple[int]

The shape of each projection defined by the Geometry object attached to this instance, as a tuple.

property sampling_kernel: ndarray[Any, dtype[float64]]

Convolution kernel for the sampling profile.

property step_size: float64

One-dimensional upsampling ratio for the integration of each projection line.

property volume_shape: Tuple[int]

The shape of the volume defined by the Geometry object attached to this instance, as a tuple.