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* Clean up and add entry * Address duplicate label warning * Add support for generic loss * Typo fix * Split loss tests out of functional tests * Minor edits * New example script * Add new example to index * Add some references * Update submodule * Typo fix * Fix import * Fix style violations * Docstring fix * Fix SVMBIRExtendedLoss.__init__ * Typo fix and minor improvement * Add pypi downloads badge * Minor docstring fix * Improve parameter names * Minor docstring improvement * Rename parameter * Update submodule
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Submodule data
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| +427 −0 | notebooks/denoise_l1tv_iso_admm.ipynb | |
| +248 −265 | notebooks/denoise_tv_iso_admm.ipynb | |
| +4 −1 | notebooks/index.ipynb |
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| .. _example_dependencies: | ||
| .. _example_depend: | ||
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| Example Dependencies | ||
| -------------------- | ||
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| #!/usr/bin/env python | ||
| # -*- coding: utf-8 -*- | ||
| # This file is part of the SCICO package. Details of the copyright | ||
| # and user license can be found in the 'LICENSE.txt' file distributed | ||
| # with the package. | ||
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| r""" | ||
| ℓ1 Total Variation (ADMM) | ||
| ========================= | ||
| This example demonstrates impulse noise removal via ℓ1 total variation | ||
| :cite:`alliney-1992-digital` :cite:`esser-2010-primal` (Sec. 2.4.4) | ||
| (i.e. total variation regularization with an ℓ1 data fidelity term), | ||
| minimizing the functional | ||
| $$\mathrm{argmin}_{\mathbf{x}} \; \| \mathbf{y} - \mathbf{x} | ||
| \|_1 + \lambda \| C \mathbf{x} \|_1 \;,$$ | ||
| where $\mathbf{y}$ is the noisy image, $C$ is a 2D finite difference | ||
| operator, and $\mathbf{x}$ is the denoised image. | ||
| """ | ||
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| import jax | ||
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| from xdesign import SiemensStar, discrete_phantom | ||
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| import scico.numpy as snp | ||
| from scico import functional, linop, loss, metric, plot | ||
| from scico.examples import spnoise | ||
| from scico.optimize.admm import ADMM, LinearSubproblemSolver | ||
| from scico.util import device_info | ||
| from scipy.ndimage import median_filter | ||
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| """ | ||
| Create a ground truth image and impose salt & pepper noise to create a | ||
| noisy test image. | ||
| """ | ||
| N = 256 # image size | ||
| phantom = SiemensStar(16) | ||
| x_gt = snp.pad(discrete_phantom(phantom, 240), 8) | ||
| x_gt = 0.5 * x_gt / x_gt.max() | ||
| x_gt = jax.device_put(x_gt) # convert to jax type, push to GPU | ||
| y = spnoise(x_gt, 0.5) | ||
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| """ | ||
| Denoise with median filtering. | ||
| """ | ||
| x_med = median_filter(y, size=(5, 5)) | ||
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| """ | ||
| Denoise with ℓ1 total variation. | ||
| """ | ||
| λ = 1.5e0 | ||
| g_loss = loss.Loss(y=y, f=functional.L1Norm()) | ||
| g_tv = λ * functional.L21Norm() | ||
| # The append=0 option makes the results of horizontal and vertical finite | ||
| # differences the same shape, which is required for the L21Norm. | ||
| C = linop.FiniteDifference(input_shape=x_gt.shape, append=0) | ||
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| solver = ADMM( | ||
| f=None, | ||
| g_list=[g_loss, g_tv], | ||
| C_list=[linop.Identity(input_shape=y.shape), C], | ||
| rho_list=[5e0, 5e0], | ||
| x0=y, | ||
| maxiter=100, | ||
| subproblem_solver=LinearSubproblemSolver(cg_kwargs={"tol": 1e-3, "maxiter": 20}), | ||
| itstat_options={"display": True, "period": 10}, | ||
| ) | ||
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| print(f"Solving on {device_info()}\n") | ||
| x_tv = solver.solve() | ||
| hist = solver.itstat_object.history(transpose=True) | ||
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| """ | ||
| Plot results. | ||
| """ | ||
| plt_args = dict(norm=plot.matplotlib.colors.Normalize(vmin=0, vmax=1.0)) | ||
| fig, ax = plot.subplots(nrows=2, ncols=2, sharex=True, sharey=True, figsize=(13, 12)) | ||
| plot.imview(x_gt, title="Ground truth", fig=fig, ax=ax[0, 0], **plt_args) | ||
| plot.imview(y, title="Noisy image", fig=fig, ax=ax[0, 1], **plt_args) | ||
| plot.imview( | ||
| x_med, | ||
| title=f"Median filtering: {metric.psnr(x_gt, x_med):.2f} (dB)", | ||
| fig=fig, | ||
| ax=ax[1, 0], | ||
| **plt_args, | ||
| ) | ||
| plot.imview( | ||
| x_tv, | ||
| title=f"ℓ1-TV denoising: {metric.psnr(x_gt, x_tv):.2f} (dB)", | ||
| fig=fig, | ||
| ax=ax[1, 1], | ||
| **plt_args, | ||
| ) | ||
| fig.show() | ||
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| """ | ||
| Plot convergence statistics. | ||
| """ | ||
| fig, ax = plot.subplots(nrows=1, ncols=2, figsize=(12, 5)) | ||
| plot.plot( | ||
| hist.Objective, | ||
| title="Objective function", | ||
| xlbl="Iteration", | ||
| ylbl="Functional value", | ||
| fig=fig, | ||
| ax=ax[0], | ||
| ) | ||
| plot.plot( | ||
| snp.vstack((hist.Prml_Rsdl, hist.Dual_Rsdl)).T, | ||
| ptyp="semilogy", | ||
| title="Residuals", | ||
| xlbl="Iteration", | ||
| lgnd=("Primal", "Dual"), | ||
| fig=fig, | ||
| ax=ax[1], | ||
| ) | ||
| fig.show() | ||
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| input("\nWaiting for input to close figures and exit") |
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