operators

Defines implementations for all operators.

All of the solvers, rely on operators including forward and adjoint operators. In tike, forward and adjoint operators are paired as fwd and adj methods of an Operator.

In this way, multiple solvers (e.g. ePIE, gradient descent, SIRT) implemented in Python can share the same core operators and can be upgraded to better operators in the future.

All operator methods accept the array type that matches the output of their asarray() method.

Operator	A base class for Operators.
Alignment	An alignment operator composed of pad, flow, and rotate operations.
Bucket	A Laminography operator.
CachedFFT	Provides a multi-plan per-device cache for CuPy FFT.
Convolution	A 2D Convolution operator with linear interpolation.
Flow	Map input 2D arrays to new coordinates by Lanczos interpolation.
Lamino	A Laminography operator.
Pad	Pad a stack of 2D images to the same shape but with unique pad_widths.
Patch	Extract (zero-padded) patches from images at provided positions.
Propagation	A Fourier-based free-space propagation using CuPy.
Ptycho	A Ptychography operator.
Rotate	Rotate a stack of 2D images along last two dimensions.
Shift	Shift last two dimensions of an array using Fourier method.

class tike.operators.Alignment

An alignment operator composed of pad, flow, and rotate operations.

The operations are applied in the aforementioned order.

Please see the help for the Pad, Flow, and Rotate operations for description of arguments.

__init__()

Please see help(Alignment) for more info.

__new__(**kwargs)

class tike.operators.Bucket

A Laminography operator.

Laminography operators to simulate propagation of the beam through the object for a defined tilt angle. An object rotates around its own vertical axis, nz, and the beam illuminates the object some tilt angle off this axis.

n

The pixel width of the cubic reconstructed grid.

Type

int

tilt

The tilt angle; the angle between the rotation axis of the object and the light source. π / 2 for conventional tomography. 0 for a beam path along the rotation axis.

Type

float32

Parameters

• u ((nz, n, n) complex64) – The complex refractive index of the object. nz is the axis corresponding to the rotation axis.

• data ((ntheta, n, n) complex64) – The complex projection data of the object.

• theta (array-like float32) – The projection angles; rotation around the vertical axis of the object.

__init__(n, tilt, eps=1, **kwargs)

Please see help(Lamino) for more info.

__new__(**kwargs)

class tike.operators.CachedFFT

Provides a multi-plan per-device cache for CuPy FFT.

A class which inherits from this class gains the _fft2, _fftn, and _ifft2 methods which provide automatic plan caching for the CuPy FFTs.

This plan cache differs from the cache included in CuPy>=8 because it is NOT per-thread. This allows us to use threadpool.map() and allows us to destroy the cache manually.

__init__()

__new__(**kwargs)

class tike.operators.Convolution

A 2D Convolution operator with linear interpolation.

Compute the product two arrays at specific relative positions.

nscan

The number of scan positions at each angular view.

Type

int

probe_shape

The pixel width and height of the (square) probe illumination.

Type

int

nz, n

The pixel width and height of the reconstructed grid.

Type

int

ntheta

The number of angular partitions of the data.

Type

int

Parameters

• psi ((..., nz, n) complex64) – The complex wavefront modulation of the object.

• probe (complex64) – The (…, nscan, nprobe, probe_shape, probe_shape) or (…, 1, nprobe, probe_shape, probe_shape) complex illumination function.

• nearplane (complex64) – The (…., nscan, nprobe, probe_shape, probe_shape) wavefronts after exiting the object.

• scan ((..., nscan, 2) float32) – Coordinates of the minimum corner of the probe grid for each measurement in the coordinate system of psi. Vertical coordinates first, horizontal coordinates second.

__init__(probe_shape, nz, n, ntheta=None, detector_shape=None, **kwargs)

__new__(**kwargs)

class tike.operators.Flow

Map input 2D arrays to new coordinates by Lanczos interpolation.

Uses Lanczos interpolation for a non-affine deformation of a series of 2D images.

__init__()

__new__(**kwargs)

class tike.operators.Lamino

A Laminography operator.

Laminography operators to simulate propagation of the beam through the object for a defined tilt angle. An object rotates around its own vertical axis, nz, and the beam illuminates the object some tilt angle off this axis.

n

The pixel width of the cubic reconstructed grid.

Type

int

tilt

The tilt angle; the angle between the rotation axis of the object and the light source. π / 2 for conventional tomography. 0 for a beam path along the rotation axis.

Type

float32 [radians]

Parameters

• u ((nz, n, n) complex64) – The complex refractive index of the object. nz is the axis corresponding to the rotation axis.

• data ((ntheta, n, n) complex64) – The complex projection data of the object.

• theta (array-like float32 [radians]) – The projection angles; rotation around the vertical axis of the object.

__init__(n, tilt, eps=0.001, upsample=1, **kwargs)

Please see help(Lamino) for more info.

__new__(**kwargs)

class tike.operators.Operator

A base class for Operators.

An Operator is a context manager which provides the basic functions (forward and adjoint) required solve an inverse problem.

Operators may be composed into other operators and inherited from to provide additional implementations to the ones provided in this library.

__init__()

__new__(**kwargs)

class tike.operators.Pad

Pad a stack of 2D images to the same shape but with unique pad_widths.

By default, no padding is applied and/or the padding is applied symmetrically.

__init__()

__new__(**kwargs)

class tike.operators.Patch

Extract (zero-padded) patches from images at provided positions.

Parameters

• images ((..., H, W) complex64) – The complex wavefront modulation of the object.

• positions ((..., N, 2) float32) – Coordinates of the minimum corner of the patches in the image grid.

• patches ((..., N * nrepeat, width+, width+) complex64) – OR (…, L, width+, width+) complex64 The extracted (zero-padded) patches. (N * nrepeat) = K * L, K >= nrepeat

• patch_width (int) – The width of the unpadded patches.

__init__()

__new__(**kwargs)

class tike.operators.Propagation

A Fourier-based free-space propagation using CuPy.

Take an (…, N, N) array and apply the Fourier transform to the last two dimensions.

detector_shape

The pixel width and height of the nearplane and farplane waves.

Type

int

cost

The function to be minimized when solving a problem.

Type

(data-like, farplane-like) -> float

grad

The gradient of cost.

Type

(data-like, farplane-like) -> farplane-like

Parameters

• nearplane ((..., detector_shape, detector_shape) complex64) – The wavefronts after exiting the object.

• farplane ((..., detector_shape, detector_shape) complex64) – The wavefronts hitting the detector respectively. Shape for cost functions and gradients is (nscan, 1, 1, detector_shape, detector_shape).

Changed in version 0.25.0: Removed the model parameter and the cost(), grad() functions. Use the cost and gradient functions directly instead.

__init__(detector_shape, norm='ortho', **kwargs)

Parameters

• detector_shape (int) –

• norm (str) –

__new__(**kwargs)

class tike.operators.Ptycho

A Ptychography operator.

Compose a diffraction and propagation operator to simulate the interaction of an illumination wavefront with an object followed by the propagation of the wavefront to a detector plane.

Parameters

• detector_shape (int) – The pixel width and height of the (square) detector grid.

• nz (int) – The pixel width and height of the reconstructed grid.

• n (int) – The pixel width and height of the reconstructed grid.

• probe_shape (int) – The pixel width and height of the (square) probe illumination.

• propagation (Operator) – The wave propagation operator being used.

• diffraction (Operator) – The object probe interaction operator being used.

• data ((..., FRAME, WIDE, HIGH) float32) – The intensity (square of the absolute value) of the propagated wavefront; i.e. what the detector records.

• farplane ((..., POSI, 1, SHARED, detector_shape, detector_shape) complex64) – The wavefronts hitting the detector respectively.

• probe ({(..., 1, 1, SHARED, WIDE, HIGH), (..., POSI, 1, SHARED, WIDE, HIGH)} complex64) – The complex illumination function.

• psi ((..., WIDE, HIGH) complex64) – The wavefront modulation coefficients of the object.

• scan ((..., POSI, 2) float32) – Coordinates of the minimum corner of the probe grid for each measurement in the coordinate system of psi. Coordinate order consistent with WIDE, HIGH order.

Changed in version 0.25.0: Removed the model and ntheta parameters.

__init__(detector_shape, probe_shape, nz, n, propagation=<class 'tike.operators.cupy.propagation.Propagation'>, diffraction=<class 'tike.operators.cupy.convolution.Convolution'>, norm='ortho', **kwargs)

Please see help(Ptycho) for more info.

Parameters

• detector_shape (int) –

• probe_shape (int) –

• nz (int) –

• n (int) –

• propagation (Type[Propagation]) –

• diffraction (Type[Convolution]) –

• norm (str) –

__new__(**kwargs)

class tike.operators.Rotate

Rotate a stack of 2D images along last two dimensions.

Parameters

• angle (float) – The desired rotation in radians. Operation skipped if angle is None.

• cval (complex64) – The value to use for filling regions that rotated from outside the original image.

__init__()

__new__(**kwargs)

class tike.operators.Shift

Shift last two dimensions of an array using Fourier method.

__init__()

__new__(**kwargs)

tike.operators.gaussian(data, intensity)

The Gaussian model objective function.

Parameters

• data ((N, M, M)) – The measured diffraction data

• intensity ((N, M, M)) – The modeled intensity

Return type

float

tike.operators.gaussian_each_pattern(data, intensity)

The Gaussian model objective function per diffraction pattern.

Parameters

• data ((N, M, M)) – The measured diffraction data

• intensity ((N, M, M)) – The modeled intensity

Returns

costs – The objective function for each pattern.

Return type

(N, )

tike.operators.gaussian_grad(data, farplane, intensity)

The gradient of the Gaussian model objective function

Parameters

• data ((N, M, M)) – The measured diffraction data

• intensity ((N, M, M)) – The modeled intensity

• farplane ((N, K, L, M, M)) –

Return type

cupy.ndarray

tike.operators.poisson(data, intensity)

The Poisson model objective function.

Parameters

• data ((N, M, M)) – The measured diffraction data

• intensity ((N, M, M)) – The modeled intensity

Return type

float

tike.operators.poisson_each_pattern(data, intensity)

The Poisson model objective function per diffraction pattern.

Parameters

• data ((N, M, M)) – The measured diffraction data

• intensity ((N, M, M)) – The modeled intensity

Returns

costs – The objective function for each pattern.

Return type

(N, )

tike.operators.poisson_grad(data, farplane, intensity)

The gradient of the Poisson model objective function.

Parameters

• data ((N, M, M)) – The measured diffraction data

• intensity ((N, M, M)) – The modeled intensity

• farplane ((N, K, L, M, M)) –

Return type

cupy.ndarray