ct_svmbir_ppp_bm3d_admm_prox.py

#!/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.

"""
CT Reconstruction (ADMM Plug-and-Play Priors w/ BM3D, SVMBIR+Prox)
==================================================================

This example demonstrates the use of class
[admm.ADMM](../_autosummary/scico.optimize.rst#scico.optimize.ADMM) to
solve a tomographic reconstruction problem using the Plug-and-Play Priors
framework :cite:`venkatakrishnan-2013-plugandplay2`, using BM3D
:cite:`dabov-2008-image` as a denoiser and SVMBIR :cite:`svmbir-2020` for
tomographic projection.

This version uses the data fidelity term as one of the ADMM g functionals,
and thus the optimization with respect to the data fidelity is able to
exploit the internal prox of the SVMBIRSquaredL2Loss functional.
"""

import numpy as np

import jax

import matplotlib.pyplot as plt
import svmbir
from xdesign import Foam, discrete_phantom

import scico.numpy as snp
from scico import metric, plot
from scico.functional import BM3D, NonNegativeIndicator
from scico.linop import Diagonal, Identity
from scico.linop.radon_svmbir import ParallelBeamProjector, SVMBIRSquaredL2Loss
from scico.optimize.admm import ADMM, LinearSubproblemSolver
from scico.util import device_info

"""
Generate a ground truth image.
"""
N = 256  # image size
density = 0.025  # attenuation density of the image
np.random.seed(1234)
x_gt = discrete_phantom(Foam(size_range=[0.05, 0.02], gap=0.02, porosity=0.3), size=N - 10)
x_gt = x_gt / np.max(x_gt) * density
x_gt = np.pad(x_gt, 5)
x_gt[x_gt < 0] = 0


"""
Generate tomographic projector and sinogram.
"""
num_angles = int(N / 2)
num_channels = N
angles = snp.linspace(0, snp.pi, num_angles, endpoint=False, dtype=snp.float32)
A = ParallelBeamProjector(x_gt.shape, angles, num_channels)
sino = A @ x_gt


"""
Impose Poisson noise on sinogram. Higher max_intensity means less noise.
"""
max_intensity = 2000
expected_counts = max_intensity * np.exp(-sino)
noisy_counts = np.random.poisson(expected_counts).astype(np.float32)
noisy_counts[noisy_counts == 0] = 1  # deal with 0s
y = -np.log(noisy_counts / max_intensity)


"""
Reconstruct using default prior of SVMBIR :cite:`svmbir-2020`.
"""
weights = svmbir.calc_weights(y, weight_type="transmission")

x_mrf = svmbir.recon(
    np.array(y[:, np.newaxis]),
    np.array(angles),
    weights=weights[:, np.newaxis],
    num_rows=N,
    num_cols=N,
    positivity=True,
    verbose=0,
)[0]


"""
Set up an ADMM solver.
"""
y, x0, weights = jax.device_put([y, x_mrf, weights])

ρ = 10  # ADMM penalty parameter
σ = density * 0.26  # denoiser sigma

f = SVMBIRSquaredL2Loss(
    y=y, A=A, W=Diagonal(weights), scale=0.5, prox_kwargs={"maxiter": 5, "ctol": 0.0}
)
g0 = σ * ρ * BM3D()
g1 = NonNegativeIndicator()

solver = ADMM(
    f=None,
    g_list=[f, g0, g1],
    C_list=[Identity(x_mrf.shape), Identity(x_mrf.shape), Identity(x_mrf.shape)],
    rho_list=[ρ, ρ, ρ],
    x0=x0,
    maxiter=20,
    subproblem_solver=LinearSubproblemSolver(cg_kwargs={"tol": 1e-3, "maxiter": 100}),
    itstat_options={"display": True},
)


"""
Run the solver.
"""
print(f"Solving on {device_info()}\n")
x_bm3d = solver.solve()
hist = solver.itstat_object.history(transpose=True)


"""
Show the recovered image.
"""
norm = plot.matplotlib.colors.Normalize(vmin=-0.1 * density, vmax=1.2 * density)
fig, ax = plt.subplots(1, 3, figsize=[15, 5])
plot.imview(img=x_gt, title="Ground Truth Image", cbar=True, fig=fig, ax=ax[0], norm=norm)
plot.imview(
    img=x_mrf,
    title=f"MRF (PSNR: {metric.psnr(x_gt, x_mrf):.2f} dB)",
    cbar=True,
    fig=fig,
    ax=ax[1],
    norm=norm,
)
plot.imview(
    img=x_bm3d,
    title=f"BM3D (PSNR: {metric.psnr(x_gt, x_bm3d):.2f} dB)",
    cbar=True,
    fig=fig,
    ax=ax[2],
    norm=norm,
)
fig.show()


"""
Plot convergence statistics.
"""
plot.plot(
    snp.vstack((hist.Prml_Rsdl, hist.Dual_Rsdl)).T,
    ptyp="semilogy",
    title="Residuals",
    xlbl="Iteration",
    lgnd=("Primal", "Dual"),
)


input("\nWaiting for input to close figures and exit")