voi?\SrSSKrSSKJr SSKJr SSKJr S Sjr S SS .S jjr SS jr g)z0Implementation of various restoration functions.N)convolve)_supported_float_type)uftcUc,[R"URURUS9up6[R "U5(d[R "X0RUS9n[UR5nURUSS9nURRUSS9nURRUSS9nURUR:wa [R "XRUS9nOUn[R"U5[R"U5S-U[R"U5S---- n U(a7[R"U [R"U5-URS9n O-[R"U [R "U5-5n U(aSXS:'SXS:'U $)uRestore image using Wiener–Hunt deconvolution. Wiener–Hunt deconvolution is a restoration method which follows a Bayesian approach [1]_. Parameters ---------- image : (N1, N2, ..., ND) ndarray Degraded image. psf : ndarray Point spread function (PSF). Assumed to be the impulse response (input image space) if the data type is real, or the transfer function (Fourier or frequency space) if the data type is complex. There is no constraint on the shape of the impulse response. The transfer function though must be of shape `(N1, N2, ..., ND)` if `is_real is True`, `(N1, N2, ..., ND // 2 + 1)` otherwise (see :func:`numpy.fft.rfftn`). balance : float Regularization parameter. Denoted by :math:`\lambda`: in the Notes section below, its value lets you balance data adequacy (improving frequency restoration) with respect to prior adequacy (reducing frequency restoration and avoiding noise artifacts). A larger value for this parameter favors the regularization/prior. reg : ndarray, optional Regularization operator. Laplacian by default. It can be an impulse response or a transfer function, as for the PSF. Shape constraints are the same as for `psf`. is_real : bool, optional True by default. Specify if `psf` and `reg` are provided over just half the frequency space (thanks to the redundancy of the Fourier transform for real signals). Applies only if `psf` and/or `reg` are provided as transfer functions. See ``uft`` module and :func:`np.fft.rfftn`. clip : bool, optional True by default. If True, pixel values of the deconvolved image (which is the return value) above 1 (resp. below -1) are clipped to 1 (resp. to -1). Be careful to set `clip=False` if you do not want this clipping and/or if your data range is not [0, 1] or [-1,1]. Returns ------- im_deconv : (N1, N2, ..., ND) ndarray The deconvolved image. Examples -------- >>> import skimage as ski >>> import scipy as sp >>> img = ski.color.rgb2gray(ski.data.astronaut()) >>> psf = np.ones((5, 5)) / 25 >>> img = sp.signal.convolve2d(img, psf, 'same') >>> rng = np.random.default_rng() >>> img += 0.1 * img.std() * rng.standard_normal(img.shape) >>> deconvolved_img = ski.restoration.wiener(img, psf, 0.1) Notes ----- This function applies the Wiener filter to a noisy (degraded) image by an impulse response (or PSF). If the data model is .. math:: y = Hx + n where :math:`n` is noise, :math:`H` the PSF, and :math:`x` the unknown original image, the Wiener filter is .. math:: \hat x = F^\dagger \left( |\Lambda_H|^2 + \lambda |\Lambda_D|^2 \right)^{-1} \Lambda_H^\dagger F y where :math:`F` and :math:`F^\dagger` are the Fourier and inverse Fourier transforms respectively, :math:`\Lambda_H` the transfer function (or the Fourier transform of the PSF, see [2]_), and :math:`\Lambda_D` the regularization operator, which is a filter penalizing the restored image frequencies (Laplacian by default, that is, penalization of high frequencies). The parameter :math:`\lambda` tunes the balance between data (which tends to increase high frequencies, even those coming from noise) and regularization/prior (which tends to avoid noise artifacts). These methods are then specific to a prior model. Consequently, the application or the true image nature must correspond to the prior model. By default, the prior model (Laplacian) introduces image smoothness or pixel correlation. It can also be interpreted as high-frequency penalization to compensate for the instability of the solution with respect to the data (sometimes called noise amplification or "explosive" solution). Finally, the use of Fourier space implies a circulant property of :math:`H`, see [2]_. 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 .. [2] B. R. Hunt "A matrix theory proof of the discrete convolution theorem", IEEE Trans. on Audio and Electroacoustics, vol. au-19, no. 4, pp. 285–288, dec. 1971 is_realFcopyrshaper)r laplacianndimrnp iscomplexobjir2tfrdtypeastyperealconjabsuirfftnurfftnuifftnufftn) imagepsfbalanceregr clip_ float_type trans_func wiener_filterdeconvs ]/var/www/html/land-ocr/venv/lib/python3.13/site-packages/skimage/restoration/deconvolution.pywienerr) s\P {uzz5;;H ??3  ii[[':&u{{3J LL%L 0E ((//*5/ 1C ((//*5/ 1C yyCIIYYsKKA  GGJ' za'BFF3K1,<"<<M]SZZ->>ekkRMCIIe,<<= z { M)rngc SSSSSS.nURU=(d 05 Uc,[R"URURUS9up([ R "U5(d[R"X RUS9n[UR5n URU SS 9nURRU SS 9nURRU SS 9nURUR:wa [R"XRUS9n OUn [ R"U RU S 9n [ R"U RU S 9n [ Rn S /S /p[ R"U5S -n[ R"U 5S -nU(a[R"U5nO[R "U5n[ R"R%U5n['US 5GH nUSU-USU--nUR)UR5nURU SS 9nUR)UR5nURU SS 9n[ R*"SU- 5USU---nUS[ R,"U 5-U- nUU-U-nUS(a US"U5 UR/UR1UR2S - S [R4"UUU -- 5- 55 UR/UR1UR2S - S - S [R4"UU-5- 55 UUS:aU U-n UUSS -:azU UUS- - nU UUS- S - - n[ R6"[ R"UU- 55[ R6"[ R"U 55- UUS- - n U n UUS:dGMXS:dGM O U WUS- - n U(a[R8"XRS9n O[R:"U 5n U(aS XS :'SXS:'XUS.4$)uUnsupervised 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, optional Dictionary of parameters for the Gibbs sampler. Accepted keys 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. 15 by default. min_num_iter : int The minimum number of iterations. 30 by default. max_num_iter : int The maximum number of iterations if ``threshold`` is not satisfied. 200 by default. callback : callable 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. clip : bool, 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 :func:`numpy.random.default_rng`). If `rng` is an int, it is used to seed the generator. .. versionadded:: 0.19 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. 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') >>> rng = np.random.default_rng() >>> img += 0.1 * img.std() * rng.standard_normal(img.shape) >>> deconvolved_img = restoration.unsupervised_wiener(img, psf) 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 g-C6?N) threshold max_num_iter min_num_iterburnincallbackr Fr rrrr1r?y?r4r3r2r0r )noiseprior)updaterrrrrrrrrrrzerosnanrurfft2ufft2random default_rngrangestandard_normalsqrtrappendgammasizeimage_quad_normsumuirfft2uifft2)rrr! user_paramsr r"r+paramsr#r$ trans_fct x_postmeanprev_x_postmeandeltagn_chaingx_chainareg2atf2 data_spectrum iteration precision_rand1_rand2 excursionr&x_samplecurrentpreviouss r(unsupervised_wienerr]sF F MM+#$ {uzz5;;H ??3  ii[[':&u{{3J LL%L 0E ((//*5/ 1C ((//*5/ 1C yyCIIIIc;;@  )//> $$]%8%89z6$$]%8%89z6GGC)O,f0DE ! rwwy'99IE !=09< *  : x (  II QC'' 98L(LMM    IIuzzA~*A0C0CHsN0S,S T vh' '(83J x(1, - Ix0@$@AG&)fX6F*F*JKHrvvg012&& +,-vh//1  % ~. .UK=P5P k3py6(+;;"&( ?# X> ??r*c[UR5nURUSS9nURUSS9n[R"UR SUS9n[R "U5nSn[U5HEn [XaSS9U-n U(a[R"X:SX - 5n OX - n U[XSS9-nMG U(aS XfS :'S XfS :'U$) aRichardson-Lucy deconvolution. Parameters ---------- image : ([P, ]M, N) ndarray Input degraded image (can be n-dimensional). If you keep the default `clip=True` parameter, you may want to normalize the image so that its values fall in the [-1, 1] interval to avoid information loss. psf : ndarray The point spread function. num_iter : int, optional Number of iterations. This parameter plays the role of regularisation. clip : bool, optional True by default. If true, pixel value of the result above 1 or under -1 are thresholded for skimage pipeline compatibility. filter_epsilon : float, optional Value below which intermediate results become 0 to avoid division by small numbers. Returns ------- im_deconv : ndarray The deconvolved image. Examples -------- >>> from skimage import img_as_float, data, restoration >>> camera = img_as_float(data.camera()) >>> from scipy.signal import convolve2d >>> psf = np.ones((5, 5)) / 25 >>> camera = convolve2d(camera, psf, 'same') >>> rng = np.random.default_rng() >>> camera += 0.1 * camera.std() * rng.standard_normal(camera.shape) >>> deconvolved = restoration.richardson_lucy(camera, psf, 5) References ---------- .. [1] https://en.wikipedia.org/wiki/Richardson%E2%80%93Lucy_deconvolution Fr r6r5g-q=same)moderrr) rrrrfullrflipr@rwhere) rrnum_iterr"filter_epsilonr$ im_deconv psf_mirrorepsr#conv relative_blurs r(richardson_lucyrkgsT'u{{3J LL%L 0E **Ze* ,C S ;IJ C 8_ V4s: HHT%:Au|LM!LMXmfEE  #$ a- $& b.! r*)NTT)NNTT)2TN) __doc__numpyr scipy.signalr _shared.utilsrrr)r]rkr*r(rss96!1BL@DU@LPU@p?r*