pd_inpainting.cc

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#include <algorithm>
#include <exception>
#include <functional>
#include <iostream>
#include <random>
#include <vector>
#include <ctime>
#include <catch2/catch_all.hpp>
 
#include "sopt/imaging_primal_dual.h"
#include "sopt/l1_non_diff_function.h"
#include "sopt/logging.h"
#include "sopt/maths.h"
#include "sopt/relative_variation.h"
#include "sopt/sampling.h"
#include "sopt/types.h"
#include "sopt/utilities.h"
#include "sopt/wavelets.h"
 
// This header is not part of the installed sopt interface
// It is only present in tests
#include "tools_for_tests/directories.h"
#include "tools_for_tests/tiffwrappers.h"
 
// \min_{x} ||\Psi^Tx||_1 \quad \mbox{s.t.} \quad ||y - Ax||_2 < \epsilon and x \geq 0
 
using Scalar = double;
using Vector = sopt::Vector<Scalar>;
using Matrix = sopt::Matrix<Scalar>;
using Image = sopt::Image<Scalar>;
 
TEST_CASE("Primal Dual Inpainting"){
  extern std::unique_ptr<std::mt19937_64> mersenne;
  std::string const input = "cameraman256";
 
  Image const image = sopt::tools::read_standard_tiff(input);
 
  sopt::t_uint const nmeasure = std::floor(0.5 * image.size());
  sopt::LinearTransform<Vector> const sampling =
      sopt::linear_transform<Scalar>(sopt::Sampling(image.size(), nmeasure, *mersenne));
 
  auto const wavelet = sopt::wavelets::factory("DB8", 4);
 
  auto const psi = sopt::linear_transform<Scalar>(wavelet, image.rows(), image.cols());
 
  Vector const y0 = sampling * Vector::Map(image.data(), image.size());
  auto constexpr snr = 30.0;
  auto const sigma = y0.stableNorm() / std::sqrt(y0.size()) * std::pow(10.0, -(snr / 20.0));
  auto const epsilon = std::sqrt(nmeasure + 2 * std::sqrt(y0.size())) * sigma;
 
  std::normal_distribution<> gaussian_dist(0, sigma);
  Vector y(y0.size());
  for (sopt::t_int i = 0; i < y0.size(); i++) y(i) = y0(i) + gaussian_dist(*mersenne);
 
  Eigen::VectorXd dirty_image = sampling.adjoint() * y;
 
  sopt::t_real const regulariser_strength = (psi.adjoint() * (sampling.adjoint() * y)).real().maxCoeff() * 1e-2;
 
  auto pd = sopt::algorithm::ImagingPrimalDual<Scalar>(y)
                        .Phi(sampling)
                        .Psi(psi)
                        .itermax(500)
                        .tau(0.5)
                        .regulariser_strength(regulariser_strength)
                        .l2ball_proximal_epsilon(epsilon)
                        .relative_variation(5e-4)
                        .residual_convergence(epsilon)
                        .positivity_constraint(true);
  
  auto const diagnostic = pd();
 
  CHECK(diagnostic.good);
  CHECK(diagnostic.niters < 500);
 
  // compare input image to cleaned output image
  // calculate mean squared error sum_i ( ( x_true(i) - x_est(i) ) **2 )
  // check this is less than the number of pixels * 0.01
  sopt::utilities::write_tiff(Matrix::Map(diagnostic.x.data(), image.rows(), image.cols()),
                                "pd_reconstruction.tiff");
  sopt::utilities::write_tiff(Matrix::Map(dirty_image.data(), image.rows(), image.cols()),
                                "pd_dirty.tiff");
  Eigen::Map<const Eigen::VectorXd> flat_image(image.data(), image.size());
  auto mse = (flat_image - diagnostic.x).array().square().sum() / image.size();
  CAPTURE(mse);
  SOPT_HIGH_LOG("MSE: {}", mse);
  CHECK(mse < 0.01);
}