padmm_reweighted_simulation.cc

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#include "purify/config.h"
#include "purify/types.h"
#include <array>
#include <ctime>
#include <memory>
#include <random>
#include <boost/math/special_functions/erf.hpp>
#include "purify/directories.h"
#include "purify/logging.h"
#include "purify/operators.h"
#include "purify/pfitsio.h"
#include "purify/utilities.h"
#include <sopt/imaging_padmm.h>
#include <sopt/positive_quadrant.h>
#include <sopt/power_method.h>
#include <sopt/relative_variation.h>
#include <sopt/reweighted.h>
#include <sopt/utilities.h>
#include <sopt/wavelets.h>
#include <sopt/wavelets/sara.h>
 
int main(int nargs, char const **args) {
  if (nargs != 8) {
    std::cerr << " Wrong number of arguments! " << '\n';
    return 1;
  }
 
  using namespace purify;
  sopt::logging::set_level("debug");
 
  std::string const kernel = args[1];
  t_real const over_sample = std::stod(static_cast<std::string>(args[2]));
  t_int const J = static_cast<t_int>(std::stod(static_cast<std::string>(args[3])));
  t_real const m_over_n = std::stod(static_cast<std::string>(args[4]));
  std::string const test_number = static_cast<std::string>(args[5]);
  t_real const ISNR = std::stod(static_cast<std::string>(args[6]));
  std::string const name = static_cast<std::string>(args[7]);
 
  std::string const fitsfile = image_filename(name + ".fits");
 
  std::string const dirty_image_fits =
      output_filename(name + "_dirty_" + kernel + "_" + test_number + ".fits");
  std::string const results =
      output_filename(name + "_results_" + kernel + "_" + test_number + ".txt");
 
  auto sky_model = pfitsio::read2d(fitsfile);
  auto sky_model_max = sky_model.array().abs().maxCoeff();
  sky_model = sky_model / sky_model_max;
  t_int const number_of_vis = std::floor(m_over_n * sky_model.size());
  t_real const sigma_m = constant::pi / 3;
  auto uv_data = utilities::random_sample_density(number_of_vis, 0, sigma_m);
  uv_data.units = utilities::vis_units::radians;
  PURIFY_MEDIUM_LOG("Number of measurements: {}", uv_data.u.size());
  auto simulate_measurements = std::get<2>(sopt::algorithm::normalise_operator<Vector<t_complex>>(
      *measurementoperator::init_degrid_operator_2d<Vector<t_complex>>(
          uv_data.u, uv_data.v, uv_data.w, uv_data.weights, sky_model.cols(), sky_model.rows(),
          over_sample, kernels::kernel_from_string.at("kb"), J, J),
      100, 1e-4, Vector<t_complex>::Random(sky_model.size())));
  uv_data.vis = simulate_measurements * sky_model;
 
  // putting measurement operator in a form that sopt can use
  auto measurements_transform = std::get<2>(sopt::algorithm::normalise_operator<Vector<t_complex>>(
      *measurementoperator::init_degrid_operator_2d<Vector<t_complex>>(
          uv_data.u, uv_data.v, uv_data.w, uv_data.weights, sky_model.cols(), sky_model.rows(),
          over_sample, kernels::kernel_from_string.at(kernel), J, J),
      100, 1e-4, Vector<t_complex>::Random(sky_model.size())));
 
  sopt::wavelets::SARA const sara{
      std::make_tuple("Dirac", 3u), std::make_tuple("DB1", 3u), std::make_tuple("DB2", 3u),
      std::make_tuple("DB3", 3u),   std::make_tuple("DB4", 3u), std::make_tuple("DB5", 3u),
      std::make_tuple("DB6", 3u),   std::make_tuple("DB7", 3u), std::make_tuple("DB8", 3u)};
 
  auto const Psi = sopt::linear_transform<t_complex>(sara, sky_model.rows(), sky_model.cols());
 
  // working out value of sigma given SNR of 30
  t_real sigma = utilities::SNR_to_standard_deviation(uv_data.vis, ISNR);
  // adding noise to visibilities
  uv_data.vis = utilities::add_noise(uv_data.vis, 0., sigma);
 
  Vector<> dimage = (measurements_transform.adjoint() * uv_data.vis).real();
  t_real const max_val = dimage.array().abs().maxCoeff();
  dimage = dimage / max_val;
  Vector<t_complex> initial_estimate = Vector<t_complex>::Zero(dimage.size());
 
  auto const epsilon = utilities::calculate_l2_radius(uv_data.vis.size(), sigma);
  auto const purify_regulariser_strength =
      (Psi.adjoint() * (measurements_transform.adjoint() * uv_data.vis).eval()).real().maxCoeff() *
      1e-3;
 
  PURIFY_HIGH_LOG("Starting sopt!");
  PURIFY_MEDIUM_LOG("Epsilon {}", epsilon);
  PURIFY_MEDIUM_LOG("Regulariser_Strength {}", purify_regulariser_strength);
  auto const padmm = sopt::algorithm::ImagingProximalADMM<t_complex>(uv_data.vis)
                         .regulariser_strength(purify_regulariser_strength)
                         .relative_variation(1e-3)
                         .l2ball_proximal_epsilon(epsilon * 1.001)
                         .tight_frame(false)
                         .l1_proximal_tolerance(1e-2)
                         .l1_proximal_nu(1)
                         .l1_proximal_itermax(50)
                         .l1_proximal_positivity_constraint(true)
                         .l1_proximal_real_constraint(true)
                         .residual_convergence(epsilon * 1.001)
                         .lagrange_update_scale(0.9)
                         .Psi(Psi)
                         .Phi(measurements_transform);
  // Timing reconstruction
  auto const posq = sopt::algorithm::positive_quadrant(padmm);
  auto const min_delta = sigma * std::sqrt(uv_data.vis.size()) / std::sqrt(9 * sky_model.size());
  // Sets weight after each padmm iteration.
  // In practice, this means replacing the proximal of the l1 objective function.
  auto const reweighted = sopt::algorithm::reweighted(padmm).min_delta(min_delta).is_converged(
      sopt::RelativeVariation<std::complex<t_real>>(1e-3));
  std::clock_t c_start = std::clock();
  auto const diagnostic = reweighted();
  std::clock_t c_end = std::clock();
 
  Image<t_complex> image =
      Image<t_complex>::Map(diagnostic.algo.x.data(), sky_model.rows(), sky_model.cols());
 
  Vector<t_complex> original = Vector<t_complex>::Map(sky_model.data(), sky_model.size(), 1);
  Image<t_complex> res = sky_model - image;
  Vector<t_complex> residual = Vector<t_complex>::Map(res.data(), image.size(), 1);
 
  auto snr = 20. * std::log10(original.norm() / residual.norm());  // SNR of reconstruction
  auto total_time = (c_end - c_start) / CLOCKS_PER_SEC;  // total time for solver to run in seconds
  // writing snr and time to a file
  std::ofstream out(results);
  out.precision(13);
  out << snr << " " << total_time;
  out.close();
 
  return 0;
}