unsupervised-wiener

unsupervised_wiener

skimage.restoration.unsupervised_wiener(image, psf, reg=None, user_params=None, is_real=True, clip=True) [source]

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:	image : (M, N) ndarray The input degraded image. psf : ndarray 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)). reg : ndarray, optional The regularisation operator. The Laplacian by default. It can be an impulse response or a transfer function, as for the psf. user_params : dict Dictionary of parameters for the Gibbs sampler. See below. clip : boolean, optional True by default. If true, pixel values of the result above 1 or under -1 are thresholded for skimage pipeline compatibility.
Returns:	x_postmean : (M, N) ndarray The deconvolved image (the posterior mean). chains : dict The keys noise and prior contain the chain list of noise and prior precision respectively.
Other Parameters:
	The keys of ``user_params`` are: threshold : float 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. burnin : int The number of sample to ignore to start computation of the mean. 100 by default. min_iter : int The minimum number of iterations. 30 by default. max_iter : int The maximum number of iterations if threshold is not satisfied. 150 by default. callback : callable (None by default) 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.

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

[R337]

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) http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-27-7-1593 http://research.orieux.fr/files/papers/OGR-JOSA10.pdf

Examples

>>> from skimage 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')
>>> img += 0.1 * img.std() * np.random.standard_normal(img.shape)
>>> deconvolved_img = restoration.unsupervised_wiener(img, psf)