skimage2.restoration.unsupervised_wiener

skimage2.restoration.unsupervised_wiener(image, psf, reg=None, user_params=None, is_real=True, clip=True, *, rng=None)

Unsupervised Wiener-Hunt deconvolution.

Return the deconvolution with a Wiener-Hunt approach, where the hyperparameters are automatically estimated. The algorithm is a stochastic iterative process (Gibbs sampler) described in the reference below. See also wiener function.

Parameters:

imagendarray of shape (M, N)

The input degraded image.

psfndarray

The impulse response (input image’s space) or the transfer function (Fourier space). Both are accepted. The transfer function is automatically recognized as being complex (np.iscomplexobj(psf)).

regndarray, optional

The regularisation operator. The Laplacian by default. It can be an impulse response or a transfer function, as for the psf.

user_paramsdict, optional

Dictionary of parameters for the Gibbs sampler. Accepted keys are:

thresholdfloat

The stopping criterion: the norm of the difference between to successive approximated solution (empirical mean of object samples, see Notes section). 1e-4 by default.

burninint

The number of sample to ignore to start computation of the mean. 15 by default.

min_num_iterint

The minimum number of iterations. 30 by default.

max_num_iterint

The maximum number of iterations if threshold is not satisfied. 200 by default.

callbackcallable

A user provided callable to which is passed, if the function exists, the current image sample for whatever purpose. The user can store the sample, or compute other moments than the mean. It has no influence on the algorithm execution and is only for inspection.

clipbool, optional

True by default. If true, pixel values of the result above 1 or under -1 are thresholded for skimage pipeline compatibility.

rng{numpy.random.Generator, int}, optional

Pseudo-random number generator. By default, a PCG64 generator is used (see numpy.random.default_rng()). If rng is an int, it is used to seed the generator.

Added in version 0.19.

Returns:

x_postmeanndarray of shape (M, N)

The deconvolved image (the posterior mean).

chainsdict

The keys noise and prior contain the chain list of noise and prior precision respectively.

Notes

The estimated image is design as the posterior mean of a probability law (from a Bayesian analysis). The mean is defined as a sum over all the possible images weighted by their respective probability. Given the size of the problem, the exact sum is not tractable. This algorithm use of MCMC to draw image under the posterior law. The practical idea is to only draw highly probable images since they have the biggest contribution to the mean. At the opposite, the less probable images are drawn less often since their contribution is low. Finally, the empirical mean of these samples give us an estimation of the mean, and an exact computation with an infinite sample set.

References

[1]

François Orieux, Jean-François Giovannelli, and Thomas Rodet, “Bayesian estimation of regularization and point spread function parameters for Wiener-Hunt deconvolution”, J. Opt. Soc. Am. A 27, 1593-1607 (2010)

https://www.osapublishing.org/josaa/abstract.cfm?URI=josaa-27-7-1593

https://hal.archives-ouvertes.fr/hal-00674508

Examples

>>> from _skimage2 import color, data, restoration
>>> img = color.rgb2gray(data.astronaut())
>>> from scipy.signal import convolve2d
>>> psf = np.ones((5, 5)) / 25
>>> img = convolve2d(img, psf, 'same')
>>> rng = np.random.default_rng()
>>> img += 0.1 * img.std() * rng.standard_normal(img.shape)
>>> deconvolved_img = restoration.unsupervised_wiener(img, psf)