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https://github.com/wassname/scikit-image.git
synced 2026-06-29 01:11:56 +08:00
Better handle of non real case. Some docstring fix.
This commit is contained in:
François Orieux
@@ -92,12 +92,14 @@ def wiener(image, psf, balance, reg=None, is_real=True):
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where :math:`n` is noise, :math:`H` the PSF and :math:`x` the
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unknown original image, the Wiener filter is
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.. math:: \hat x = F^\dag (|\Lambda_H|^2 + \lambda |\Lambda_D|^2) \Lambda_H^\dag F y
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.. math::
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\hat x = F^\dag (|\Lambda_H|^2 + \lambda |\Lambda_D|^2)
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\Lambda_H^\dag F y
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where :math:`F` and :math:`F^\dag` are the Fourier and inverse
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Fourier transfroms respectively, :math:`\Lambda_H` the transfer
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function (or the Fourier transfrom of the PSF, see [2]) and
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:math:`\Lambda_D` the filter to penalize the restored image
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function (or the Fourier transfrom of the PSF, see [Hunt] below)
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and :math:`\Lambda_D` the filter to penalize the restored image
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frequencies (Laplacian by default, that is penalization of high
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frequency). The parameter :math:`\lambda` tunes the balance
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between the data (that tends to increase high frequency, even
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@@ -110,9 +112,9 @@ def wiener(image, psf, balance, reg=None, is_real=True):
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as high-frequency penalization to compensate noise amplification
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or so called "explosive" solution. These methods are well
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interpreted by Bayesian analysis.
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Finally, the use of Fourier space implies a circulant property of
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:math:`H`, see [2].
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:math:`H`, see [Hunt].
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References
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----------
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@@ -128,15 +130,14 @@ def wiener(image, psf, balance, reg=None, is_real=True):
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.. [2] B. R. Hunt "A matrix theory proof of the discrete
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convolution theorem", IEEE Trans. on Audio and
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Electroacoustics, vol. au-19, no. 4, pp. 285-288, dec. 1971
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"""
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if reg is None:
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reg, _ = uft.laplacian(image.ndim, image.shape)
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reg, _ = uft.laplacian(image.ndim, image.shape, is_real=is_real)
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if not np.iscomplexobj(reg):
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reg = uft.ir2tf(reg, image.shape)
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reg = uft.ir2tf(reg, image.shape, is_real=is_real)
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if psf.shape != reg.shape:
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trans_func = uft.ir2tf(psf, image.shape)
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trans_func = uft.ir2tf(psf, image.shape, is_real=is_real)
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else:
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trans_func = psf
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@@ -148,7 +149,7 @@ def wiener(image, psf, balance, reg=None, is_real=True):
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return uft.uifft2(wiener_filter * uft.ufft2(image))
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def unsupervised_wiener(image, psf, reg=None, user_params=None):
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def unsupervised_wiener(image, psf, reg=None, user_params=None, is_real=True):
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"""Unsupervised Wiener-Hunt deconvolution
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Return the deconvolution with a Wiener-Hunt approach, where the
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@@ -240,12 +241,12 @@ def unsupervised_wiener(image, psf, reg=None, user_params=None):
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params.update(user_params or {})
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if reg is None:
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reg, _ = uft.laplacian(image.ndim, image.shape)
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reg, _ = uft.laplacian(image.ndim, image.shape, is_real=is_real)
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if not np.iscomplexobj(reg):
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reg = uft.ir2tf(reg, image.shape)
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reg = uft.ir2tf(reg, image.shape, is_real=is_real)
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if psf.shape != reg.shape:
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trans_fct = uft.ir2tf(psf, image.shape)
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trans_fct = uft.ir2tf(psf, image.shape, is_real=is_real)
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else:
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trans_fct = psf
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@@ -267,13 +268,16 @@ def unsupervised_wiener(image, psf, reg=None, user_params=None):
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# The Fourier transfrom may change the image.size attribut, so we
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# store it.
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data_spectrum = uft.urfft2(image.astype(np.float))
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if is_real:
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data_spectrum = uft.urfft2(image.astype(np.float))
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else:
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data_spectrum = uft.ufft2(image.astype(np.float))
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# Gibbs sampling
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for iteration in range(params['max_iter']):
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# Sample of Eq. 27 p(circX^k | gn^k-1, gx^k-1, y).
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# weighing (correlation in direct space)
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# weighting (correlation in direct space)
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precision = gn_chain[-1] * atf2 + gx_chain[-1] * areg2 # Eq. 29
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excursion = np.sqrt(0.5) / np.sqrt(precision) * (
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np.random.standard_normal(data_spectrum.shape) +
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@@ -316,7 +320,10 @@ def unsupervised_wiener(image, psf, reg=None, user_params=None):
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# Empirical average \approx POSTMEAN Eq. 44
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x_postmean = x_postmean / (iteration - params['burnin'])
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x_postmean = uft.uirfft2(x_postmean)
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if is_real:
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x_postmean = uft.uirfft2(x_postmean)
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else:
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x_postmean = uft.uifft2(x_postmean)
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return (x_postmean, {'noise': gn_chain, 'prior': gx_chain})
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@@ -343,7 +343,7 @@ def image_quad_norm(inarray):
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-------
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norm : float
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The quadratic norm of `inarray`.
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Examples
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--------
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>>> input = np.ones((5, 5))
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@@ -360,7 +360,7 @@ def image_quad_norm(inarray):
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return np.sum(np.sum(np.abs(inarray)**2, axis=-1), axis=-1)
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def ir2tf(imp_resp, shape, dim=None, real=True):
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def ir2tf(imp_resp, shape, dim=None, is_real=True):
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"""Compute the transfer function of IR
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This function make the necessary correct zero-padding, zero
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@@ -378,7 +378,7 @@ def ir2tf(imp_resp, shape, dim=None, real=True):
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dim : int, optional
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The `dim` last axis along wich to compute the transform. All
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axes by default.
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real : boolean (optionnal, default True)
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is_real : boolean (optionnal, default True)
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If True, imp_resp is supposed real and the hermissian property
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is used with rfftn Fourier transform.
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@@ -395,6 +395,10 @@ def ir2tf(imp_resp, shape, dim=None, real=True):
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--------
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>>> np.all(np.array([[4, 0], [0, 0]]) == ir2tf(np.ones((2, 2)), (2, 2)))
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True
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>>> ir2tf(np.ones((2, 2)), (512, 512)).shape == (512, 257)
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True
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>>> ir2tf(np.ones((2, 2)), (512, 512), is_real=False).shape == (512, 512)
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True
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Notes
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-----
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@@ -416,13 +420,13 @@ def ir2tf(imp_resp, shape, dim=None, real=True):
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irpadded = np.roll(irpadded,
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shift=-int(np.floor(axis_size / 2)),
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axis=axis)
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if real:
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if is_real:
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return np.fft.rfftn(irpadded, axes=range(-dim, 0))
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else:
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return np.fft.fftn(irpadded, axes=range(-dim, 0))
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def laplacian(ndim, shape):
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def laplacian(ndim, shape, is_real=True):
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"""Return the transfert function of the laplacian
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Laplacian is the second order difference, on line and column.
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@@ -433,6 +437,10 @@ def laplacian(ndim, shape):
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The dimension of the laplacian
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shape : tuple, shape
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The support on which to compute the transfert function
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is_real : boolean (optionnal, default True)
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If True, imp_resp is supposed real and the hermissian property
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is used with rfftn Fourier transform to return the transfert
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function.
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Returns
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-------
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@@ -440,7 +448,7 @@ def laplacian(ndim, shape):
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The transfert function
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impr : array_like, real
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The laplacian
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Examples
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--------
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>>> tf, ir = laplacian(2, (32, 32))
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@@ -459,4 +467,4 @@ def laplacian(ndim, shape):
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-1.0]).reshape([-1 if i == dim else 1
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for i in range(ndim)])
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impr[([slice(1, 2)] * ndim)] = 2.0 * ndim
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return ir2tf(impr, shape), impr
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return ir2tf(impr, shape, is_real=is_real), impr
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