2.1.4.1.5. sf_tools.math.stats module

STATISTICS ROUTINES

This module contains methods for basic statistics.

Author:Samuel Farrens <samuel.farrens@gmail.com> Version:1.2 Date:20/10/2017

sf_tools.math.stats.chi2_gof(data_obs, data_exp, sigma, ddof=1)

Chi-squared goodness-of-fit

This method tests the chi^2 goodness of fit.

Parameters:

• data_obs (np.ndarray) – Observed data array
• data_exp (np.ndarray) – Expected data array
• sigma (float) – Expected data error
• ddof (input) – Delta degrees of freedom. Default (ddof = 1).

Returns:

Return type:

tuple of floats chi-squared and P values

sf_tools.math.stats.gaussian(point, mean, sigma, amplitude=None)

Gaussian distribution

Method under development…

sf_tools.math.stats.gaussian_kernel(data_shape, sigma, norm='max')

Gaussian kernel

This method produces a Gaussian kerenal of a specified size and dispersion

Parameters:

• data_shape (tuple) – Desiered shape of the kernel
• sigma (float) – Standard deviation of the kernel
• norm (str {'max', 'sum'}, optional) – Normalisation of the kerenl (options are ‘max’ or ‘sum’)

Returns:

Return type:

np.ndarray kernel

sf_tools.math.stats.mad(data)

Median absolute deviation

This method calculates the median absolute deviation of the input data.

Parameters:data (np.ndarray) – Input data array Returns: Return type:float MAD value

Notes

The MAD is calculated as follows:

\[\mathrm{MAD} = \mathrm{median}\left(|X_i - \mathrm{median}(X)|\right)\]

sf_tools.math.stats.mse(data1, data2)

Mean Squared Error

This method returns the Mean Squared Error (MSE) between two data sets.

Parameters:

• data1 (np.ndarray) – First data set
• data2 (np.ndarray) – Second data set

sf_tools.math.stats.psnr2(image, noisy_image, max_pix=255)

Peak Signal-to-Noise Ratio

This method calculates the PSNR between an image and a noisy version of that image

Parameters:

• image (np.ndarray) – Input image, 2D array
• noisy_image (np.ndarray) – Noisy image, 2D array
• max_pix (int) – Maximum number of pixels. Default (max_pix=255)

Returns:

Return type:

float PSNR value

Notes

Implements PSNR equation on https://en.wikipedia.org/wiki/Peak_signal-to-noise_ratio

\[\mathrm{PSNR} = 20\log_{10}(\mathrm{MAX}_I - 10\log_{10}(\mathrm{MSE}))\]

sf_tools.math.stats.psnr(image, recovered_image)

Peak Signal-to-Noise Ratio

This method calculates the PSNR between an image and the recovered version of that image

Parameters:

• image (np.ndarray) – Input image, 2D array
• recovered_image (np.ndarray) – Recovered image, 2D array

Returns:

Return type:

float PSNR value

Notes

Implements eq.3.7 from _[S2010]

sf_tools.math.stats.psnr_stack(images, recoverd_images, metric=<function mean>)

Peak Signa-to-Noise for stack of images

This method calculates the PSNRs for a stack of images and the corresponding recovered images. By default the metod returns the mean value of the PSNRs, but any other metric can be used.

Parameters:

• images (np.ndarray) – Stack of images, 3D array
• recovered_images (np.ndarray) – Stack of recovered images, 3D array
• metric (function) – The desired metric to be applied to the PSNR values (default is ‘np.mean’)

Returns:

Return type:

float metric result of PSNR values

Raises:

ValueError – For invalid input data dimensions

sf_tools.math.stats.sigma_mad(data)

Standard deviation from MAD

This method calculates the standard deviation of the input data from the MAD.

Parameters:data (np.ndarray) – Input data array Returns: Return type:float sigma value

Notes

This function can be used for estimating the standeviation of the noise in imgaes.

Sigma is calculated as follows:

\[\sigma = 1.4826 \mathrm{MAD}(X)\]