pyextal.LucyRichardson¶

Attributes¶

_CONVOLUTIONS

Functions¶

`sgnoise`(img, m, g, A, delta, varB)	Calculates the signal-dependent noise.
`DQE`(img, varB, delta, A)	Calculates the Detective Quantum Efficiency (DQE).
`chisq2d`(exp, convolved, bval, m, g, A, delta, varB)	Calculates the 2D chi-squared value.
`convolved2d`(img, mtf)	Performs a 2D convolution using FFT.
`convolved2d_real`(img, mtf)	Performs a 2D convolution in real space.
`lucy_Richardson`(dp, mtf, background, niter[, varB, ...])	Performs Lucy-Richardson deconvolution.

Module Contents¶

pyextal.LucyRichardson.sgnoise(img, m, g, A, delta, varB)¶

Calculates the signal-dependent noise.

Parameters:

img (np.ndarray) – The input image.
m (float) – Mixing factor.
g (float) – Gain.
A (float) – A parameter related to Fano noise and conversion gain.
delta (float) – Squared percentage error in the gain image.
varB (float) – Variance of the background.

Returns:

The calculated signal-dependent noise.

Return type:

np.ndarray

pyextal.LucyRichardson.DQE(img, varB, delta, A)¶

Calculates the Detective Quantum Efficiency (DQE).

Parameters:

img (np.ndarray) – The input image.
varB (float) – Variance of the background.
delta (float) – Squared percentage error in the gain image.
A (float) – A parameter related to Fano noise and conversion gain.

Returns:

The calculated DQE.

Return type:

np.ndarray

pyextal.LucyRichardson.chisq2d(exp, convolved, bval, m, g, A, delta, varB)¶

Calculates the 2D chi-squared value.

Parameters:

exp (np.ndarray) – The experimental data.
convolved (np.ndarray) – The convolved model.
bval (np.ndarray) – The background values.
m (float) – Mixing factor.
g (float) – Gain.
A (float) – A parameter related to Fano noise and conversion gain.
delta (float) – Squared percentage error in the gain image.
varB (float) – Variance of the background.

Returns:

The calculated chi-squared value.

Return type:

float

pyextal.LucyRichardson.convolved2d(img, mtf)¶

Performs a 2D convolution using FFT.

mtf is taken to be already in the Fourier domain and to have the same shape as img — this is what pyextal.larbed.LARBEDCalibration.calculate_mtf() produces.

Parameters:

img (np.ndarray) – The input image.
mtf (np.ndarray) – The modulation transfer function, in the Fourier domain.

Returns:

The convolved image.

Return type:

np.ndarray

pyextal.LucyRichardson.convolved2d_real(img, mtf)¶

Performs a 2D convolution in real space.

mtf is taken to be a real-space kernel. This is the convolution used by the standalone PyLARBED package and is kept so that results produced with it can be reproduced exactly; see the mode argument of lucy_Richardson().

Parameters:

img (np.ndarray) – The input image.
mtf (np.ndarray) – The modulation transfer function, as a real-space kernel.

Returns:

The convolved image, cropped to the shape of img.

Return type:

np.ndarray

pyextal.LucyRichardson._CONVOLUTIONS¶

pyextal.LucyRichardson.lucy_Richardson(dp, mtf, background, niter, varB=0, delta=0, A=1, g=1, m=1, mode='fourier')¶

Performs Lucy-Richardson deconvolution.

Parameters:

dp (np.ndarray) – The diffraction pattern.
mtf (np.ndarray) – The modulation transfer function. Interpreted as a Fourier-domain array when mode='fourier' and as a real-space kernel when mode='real'.
background (np.ndarray) – The background of the diffraction pattern.
niter (int) – The number of iterations.
varB (float, optional) – Variance of the background. Defaults to 0.
delta (float, optional) – The squared percentage error in the gain image. Defaults to 0.
A (float, optional) – A parameter related to Fano noise and conversion gain, given by \(1 + F + \frac{1}{mG}\). Defaults to 1.
g (float, optional) – The gain. Defaults to 1.
m (float, optional) – The mixing factor. Defaults to 1.
mode (str, optional) – 'fourier' to convolve via FFT, 'real' to convolve in real space. Defaults to 'fourier'.

Returns:

The deconvolved image.

Return type:

np.ndarray

Raises:

ValueError – If mode is not 'fourier' or 'real'.