mirror of
https://github.com/wassname/scikit-image.git
synced 2026-07-20 12:40:31 +08:00
François Orieux
33aedfd9aa
This module add three function to skimage. The `wiener` function is a simple wiener deconvolution. The `unsupervised_wiener` is a more sophisticated wiener deconvolution with automatic estimation of regularisation parameters. The third function is a literal traduction in python of the rychardson lucy deconvolution of wikipedia.
326 lines
10 KiB
Python
326 lines
10 KiB
Python
# -*- coding: utf-8 -*-
|
||
|
||
# Copyright (c) 2013 François Orieux <orieux@iap.fr>
|
||
|
||
# Permission is hereby granted, free of charge, to any person
|
||
# obtaining a copy of this software and associated documentation files
|
||
# (the "Software"), to deal in the Software without restriction,
|
||
# including without limitation the rights to use, copy, modify, merge,
|
||
# publish, distribute, sublicense, and/or sell copies of the Software,
|
||
# and to permit persons to whom the Software is furnished to do so,
|
||
# subject to the following conditions:
|
||
|
||
# The above copyright notice and this permission notice shall be
|
||
# included in all copies or substantial portions of the Software.
|
||
|
||
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
|
||
# EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
|
||
# MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
|
||
# NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
|
||
# BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
|
||
# ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
|
||
# CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
|
||
# SOFTWARE.
|
||
|
||
# Commentary:
|
||
|
||
"""Implementations deconvolution functions"""
|
||
|
||
# code:
|
||
|
||
from __future__ import division
|
||
|
||
import numpy as np
|
||
import numpy.random as npr
|
||
from scipy.signal import convolve2d as conv2
|
||
|
||
import uft
|
||
|
||
__author__ = "François Orieux"
|
||
__copyright__ = "Copyright (C) 2013 F. Orieux <orieux@iap.fr>"
|
||
__credits__ = ["François Orieux"]
|
||
__license__ = "mit"
|
||
__version__ = "0.1.0"
|
||
__maintainer__ = "François Orieux"
|
||
__email__ = "orieux@iap.fr"
|
||
__status__ = "stable"
|
||
__url__ = "http://research.orieux.fr"
|
||
__keywords__ = "deconvolution, image"
|
||
|
||
|
||
def wiener(data, psf, reg_val, reg=None, real=True):
|
||
"""Wiener-Hunt deconvolution
|
||
|
||
return the deconvolution with a wiener-hunt approach (ie with
|
||
Fourier diagonalisation).
|
||
|
||
Parameters
|
||
----------
|
||
data : (M, N) ndarray
|
||
The data
|
||
|
||
psf : ndarray
|
||
The impulsionnal response in real space or the transfer
|
||
function. Differentiation is done with the dtype where
|
||
transfer function is supposed complex.
|
||
|
||
reg_val : float
|
||
The regularisation parameter value.
|
||
|
||
reg : ndarray, optional
|
||
The regularisation operator. The laplacian by
|
||
default. Otherwise, the same constraints that for `psf`
|
||
apply.
|
||
|
||
real : boolean, optional
|
||
True by default. Specify if `psf` or `reg` are provided
|
||
with hermitian hypothesis or not. See uft module.
|
||
|
||
Returns
|
||
-------
|
||
im_deconv : (M, N) ndarray
|
||
The deconvolued data
|
||
|
||
Exemples
|
||
--------
|
||
>>> from skimage import color, data, deconvolution
|
||
>>> lena = color.rgb2gray(data.lena())
|
||
>>> from scipy.signal import convolve2d as conv2
|
||
>>> psf = np.ones((5, 5))
|
||
>>> lena = conv2(lena, psf, 'same')
|
||
>>> lena += 0.1 * lena.std() * np.random.standard_normal(lena.shape)
|
||
>>> deconvolued_lena = deconvolution.wiener(lena, psf, 1100)
|
||
|
||
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)
|
||
|
||
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-27-7-1593
|
||
|
||
.. [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
|
||
"""
|
||
if not reg:
|
||
reg, _ = uft.laplacian(data.ndim, data.shape)
|
||
if reg.dtype != np.complex:
|
||
reg = uft.ir2tf(reg, data.shape)
|
||
|
||
if psf.shape != reg.shape:
|
||
trans_func = uft.ir2tf(psf, data.shape)
|
||
else:
|
||
trans_func = psf
|
||
|
||
wiener_filter = np.conj(trans_func) / (np.abs(trans_func)**2 +
|
||
reg_val * np.abs(reg)**2)
|
||
if real:
|
||
return uft.uirfft2(wiener_filter * uft.urfft2(data))
|
||
else:
|
||
return uft.uifft2(wiener_filter * uft.ufft2(data))
|
||
|
||
|
||
def unsupervised_wiener(data, psf, reg=None, user_params=None):
|
||
"""Unsupervised Wiener-Hunt deconvolution
|
||
|
||
return the deconvolution with a wiener-hunt approach, where the
|
||
hyperparameters are estimated (or automatically tuned from a
|
||
practical point of view). The algorithm is a stochastic iterative
|
||
process (Gibbs sampler).
|
||
|
||
If you use this work, please add a citation to the reference below.
|
||
|
||
Parameters
|
||
----------
|
||
image : (M, N) ndarray
|
||
The data
|
||
|
||
psf : ndarray
|
||
The impulsionnal response in real space or the transfer
|
||
function. Differentiation is done with the dtype where
|
||
transfer function is supposed complex.
|
||
|
||
reg : ndarray, optional
|
||
The regularisation operator. The laplacian by
|
||
default. Otherwise, the same constraints that for `psf`
|
||
apply
|
||
|
||
user_params : dict
|
||
dictionary of gibbs parameters. See below.
|
||
|
||
Returns
|
||
-------
|
||
x_postmean : (M, N) ndarray
|
||
The deconvolued data (the posterior mean)
|
||
|
||
chains : dict
|
||
The keys 'noise' and 'prior' contains the chain list of noise and
|
||
prior precision respectively
|
||
|
||
Other parameters
|
||
----------------
|
||
The key of user_params are
|
||
|
||
threshold : float
|
||
The stopping criterion: the norm of the difference between to
|
||
successive approximated solution (empirical mean of object
|
||
sample). 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 iteration. 30 by default.
|
||
|
||
max_iter : int
|
||
The maximum number of iteration if `threshold` is not
|
||
satisfied. 150 by default.
|
||
|
||
callback : None
|
||
A user provided callable to which is passed, if the function
|
||
exists, the current image sample. This function can be used to
|
||
store the sample, or compute other moments than the mean.
|
||
|
||
Exemples
|
||
--------
|
||
>>> from skimage import color, data, deconvolution
|
||
>>> lena = color.rgb2gray(data.lena())
|
||
>>> from scipy.signal import convolve2d as conv2
|
||
>>> psf = np.ones((5, 5))
|
||
>>> lena = conv2(lena, psf, 'same')
|
||
>>> lena += 0.1 * lena.std() * np.random.standard_normal(lena.shape)
|
||
>>> deconvolued_lena = deconvolution.unsupervised_wiener(lena, psf)
|
||
|
||
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)
|
||
|
||
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-27-7-1593
|
||
"""
|
||
params = {'threshold': 1e-4, 'max_iter': 200,
|
||
'min_iter': 30, 'burnin': 15, 'callback': None}
|
||
params.update(user_params if user_params else {})
|
||
|
||
if not reg:
|
||
reg, _ = uft.laplacian(data.ndim, data.shape)
|
||
if reg.dtype != np.complex:
|
||
reg = uft.ir2tf(reg, data.shape)
|
||
|
||
if psf.shape != reg.shape:
|
||
trans_fct = uft.ir2tf(psf, data.shape)
|
||
else:
|
||
trans_fct = psf
|
||
|
||
# The mean of the object
|
||
x_postmean = np.zeros(trans_fct.shape)
|
||
# The previous computed mean in the iterative loop
|
||
prev_x_postmean = np.zeros(trans_fct.shape)
|
||
|
||
# Difference between two successive mean
|
||
delta = np.NAN
|
||
|
||
# Initial state of the chain
|
||
gn_chain, gx_chain = [1], [1]
|
||
|
||
# The correlation of the object in Fourier space (if size is big,
|
||
# this can reduce computation time in the loop)
|
||
areg2 = np.abs(reg)**2
|
||
atf2 = np.abs(trans_fct)**2
|
||
|
||
data = uft.urfft2(data.astype(np.float))
|
||
|
||
# Gibbs sampling
|
||
for iteration in range(params['max_iter']):
|
||
# Sample of Eq. 27 p(circX^k | gn^k-1, gx^k-1, y).
|
||
|
||
# weighing (correlation in direct space)
|
||
precision = gn_chain[-1] * atf2 + gx_chain[-1] * areg2 # Eq. 29
|
||
excursion = uft.crandn(data.shape) / np.sqrt(precision)
|
||
|
||
# mean Eq. 30 (RLS for fixed gn, gamma0 and gamma1 ...)
|
||
wiener_filter = gn_chain[-1] * np.conj(trans_fct) / precision
|
||
|
||
# sample of X in Fourier space
|
||
x_sample = wiener_filter * data + excursion
|
||
if params['callback']:
|
||
params['callback'](x_sample)
|
||
|
||
# sample of Eq. 31 p(gn | x^k, gx^k, y)
|
||
gn_chain.append(npr.gamma(data.size / 2,
|
||
2 / uft.image_quad_norm(data - x_sample *
|
||
trans_fct)))
|
||
|
||
# sample of Eq. 31 p(gx | x^k, gn^k-1, y)
|
||
gx_chain.append(npr.gamma((data.size - 1) / 2,
|
||
2 / uft.image_quad_norm(x_sample * reg)))
|
||
|
||
# current empirical average
|
||
if iteration > params['burnin']:
|
||
x_postmean = prev_x_postmean + x_sample
|
||
|
||
if iteration > (params['burnin'] + 1):
|
||
current = x_postmean / (iteration - params['burnin'])
|
||
previous = prev_x_postmean / (iteration - params['burnin'] - 1)
|
||
|
||
delta = np.sum(np.abs(current - previous)) / \
|
||
np.sum(np.abs(x_postmean)) / (iteration - params['burnin'])
|
||
|
||
prev_x_postmean = x_postmean
|
||
|
||
# stop of the algorithm
|
||
if (iteration > params['min_iter']) and (delta < params['threshold']):
|
||
break
|
||
|
||
# Empirical average \approx POSTMEAN Eq. 44
|
||
x_postmean = x_postmean / (iteration - params['burnin'])
|
||
x_postmean = uft.uirfft2(x_postmean)
|
||
|
||
return (x_postmean, {'noise': gn_chain, 'prior': gx_chain})
|
||
|
||
|
||
def richardson_lucy(data, psf, iterations=50):
|
||
"""Richardson lucy deconvolution
|
||
|
||
This a python conversion of the wikipedia page on this algorithm. See
|
||
|
||
http://en.wikipedia.org/wiki/Richardson%E2%80%93Lucy_deconvolution
|
||
|
||
Parameters
|
||
----------
|
||
data : ndarray
|
||
The data
|
||
|
||
psf : ndarray
|
||
The impulsionnal response in real space.
|
||
|
||
iterations : int
|
||
dictionary of gibbs parameters. See below.
|
||
|
||
Returns
|
||
-------
|
||
im_deconv : ndarray
|
||
The deconvolued image
|
||
|
||
References
|
||
----------
|
||
.. [2] Richardson, William Hadley, "Bayesian-Based Iterative
|
||
Method of Image Restoration". JOSA 62 (1):
|
||
55–59. doi:10.1364/JOSA.62.000055, 1972
|
||
|
||
"""
|
||
data = data.astype(np.float)
|
||
psf = psf.astype(np.float)
|
||
im_deconv = 0.5 * np.ones(data.shape)
|
||
psf_mirror = psf[::-1, ::-1]
|
||
for iteration in range(iterations):
|
||
relative_blur = data / conv2(im_deconv, psf, 'same')
|
||
im_deconv *= conv2(relative_blur, psf_mirror, 'same')
|
||
|
||
return im_deconv
|