1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
|
#include "purify/types.h"
#include <array>
#include <memory>
#include <random>
#include <boost/filesystem.hpp>
#include <boost/math/special_functions/erf.hpp>
#include "purify/directories.h"
#include "purify/distribute.h"
#include "purify/logging.h"
#include "purify/mpi_utilities.h"
#include "purify/operators.h"
#include "purify/pfitsio.h"
#include "purify/read_measurements.h"
#include "purify/utilities.h"
#include <sopt/imaging_padmm.h>
#include <sopt/mpi/communicator.h>
#include <sopt/mpi/session.h>
#include <sopt/power_method.h>
#include <sopt/relative_variation.h>
#include <sopt/utilities.h>
#include <sopt/wavelets.h>
#include <sopt/wavelets/sara.h>
#ifdef PURIFY_GPU
#include "purify/operators_gpu.h"
#endif
#ifndef PURIFY_PADMM_ALGORITHM
#define PURIFY_PADMM_ALGORITHM 2
#endif
using namespace purify;
using namespace purify::notinstalled;
std::tuple<utilities::vis_params, t_real> dirty_visibilities(
Image<t_complex> const &ground_truth_image, t_uint number_of_vis, t_real snr,
const std::tuple<bool, t_real> &w_term) {
auto uv_data =
utilities::random_sample_density(number_of_vis, 0, constant::pi / 3, std::get<0>(w_term));
uv_data.units = utilities::vis_units::radians;
PURIFY_HIGH_LOG("Number of measurements / number of pixels: {}",
uv_data.u.size() / ground_truth_image.size());
// creating operator to generate measurements
auto const sky_measurements = std::get<2>(sopt::algorithm::normalise_operator<Vector<t_complex>>(
measurementoperator::init_degrid_operator_2d<Vector<t_complex>>(
uv_data, ground_truth_image.rows(), ground_truth_image.cols(), std::get<1>(w_term),
std::get<1>(w_term), 2, kernels::kernel::kb, 8, 8, std::get<0>(w_term)),
100, 1e-4, Vector<t_complex>::Random(ground_truth_image.size())));
// Generates measurements from image
uv_data.vis = (*sky_measurements) *
Image<t_complex>::Map(ground_truth_image.data(), ground_truth_image.size(), 1);
// working out value of signal given SNR of 30
auto const sigma = utilities::SNR_to_standard_deviation(uv_data.vis, snr);
// adding noise to visibilities
uv_data.vis = utilities::add_noise(uv_data.vis, 0., sigma);
return std::make_tuple(uv_data, sigma);
}
std::tuple<utilities::vis_params, t_real> dirty_visibilities(
Image<t_complex> const &ground_truth_image, t_uint number_of_vis, t_real snr,
const std::tuple<bool, t_real> &w_term, sopt::mpi::Communicator const &comm) {
if (comm.size() == 1) return dirty_visibilities(ground_truth_image, number_of_vis, snr, w_term);
if (comm.is_root()) {
auto result = dirty_visibilities(ground_truth_image, number_of_vis, snr, w_term);
comm.broadcast(std::get<1>(result));
auto const order =
distribute::distribute_measurements(std::get<0>(result), comm, distribute::plan::radial);
std::get<0>(result) = utilities::regroup_and_scatter(std::get<0>(result), order, comm);
return result;
}
auto const sigma = comm.broadcast<t_real>();
return std::make_tuple(utilities::scatter_visibilities(comm), sigma);
}
std::shared_ptr<sopt::algorithm::ImagingProximalADMM<t_complex>> padmm_factory(
std::shared_ptr<sopt::LinearTransform<Vector<t_complex>> const> const &measurements,
const sopt::wavelets::SARA &sara, const Image<t_complex> &ground_truth_image,
const utilities::vis_params &uv_data, const t_real sigma, const sopt::mpi::Communicator &comm) {
auto const Psi = sopt::linear_transform<t_complex>(sara, ground_truth_image.rows(),
ground_truth_image.cols(), comm);
#if PURIFY_PADMM_ALGORITHM == 2
auto const epsilon = std::sqrt(
comm.all_sum_all(std::pow(utilities::calculate_l2_radius(uv_data.vis.size(), sigma), 2)));
#elif PURIFY_PADMM_ALGORITHM == 3 || PURIFY_PADMM_ALGORITHM == 1
auto const epsilon = utilities::calculate_l2_radius(uv_data.vis.size(), sigma);
#endif
PURIFY_LOW_LOG("SARA Size = {}, Rank = {}", sara.size(), comm.rank());
const t_real gamma =
utilities::step_size(uv_data.vis, measurements,
std::make_shared<sopt::LinearTransform<Vector<t_complex>> const>(Psi),
sara.size()) *
1e-3;
PURIFY_LOW_LOG("Epsilon {}, Rank = {}", epsilon, comm.rank());
PURIFY_LOW_LOG("Gamma {}, SARA Size = {}, Rank = {}", gamma, sara.size(), comm.rank());
// shared pointer because the convergence function need access to some data that we would rather
// not reproduce. E.g. padmm definition is self-referential.
auto padmm = std::make_shared<sopt::algorithm::ImagingProximalADMM<t_complex>>(uv_data.vis);
padmm->itermax(50)
.gamma(comm.all_reduce(gamma, MPI_MAX))
.relative_variation(1e-3)
.l2ball_proximal_epsilon(epsilon)
#if PURIFY_PADMM_ALGORITHM == 2
// communicator ensuring l2 norm in l2ball proximal is global
.l2ball_proximal_communicator(comm)
#endif
// communicator ensuring l1 norm in l1 proximal is global
.l1_proximal_adjoint_space_comm(comm)
.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_tolerance(epsilon)
.lagrange_update_scale(0.9)
.nu(1e0)
.Psi(Psi)
.Phi(*measurements);
sopt::ScalarRelativeVariation<t_complex> conv(padmm->relative_variation(),
padmm->relative_variation(), "Objective function");
std::weak_ptr<decltype(padmm)::element_type> const padmm_weak(padmm);
padmm->residual_convergence([padmm_weak, conv, comm](
Vector<t_complex> const &x,
Vector<t_complex> const &residual) mutable -> bool {
auto const padmm = padmm_weak.lock();
#if PURIFY_PADMM_ALGORITHM == 2
auto const residual_norm = sopt::mpi::l2_norm(residual, padmm->l2ball_proximal_weights(), comm);
auto const result = residual_norm < padmm->residual_tolerance();
#elif PURIFY_PADMM_ALGORITHM == 3 || PURIFY_PADMM_ALGORITHM == 1
auto const residual_norm = sopt::l2_norm(residual, padmm->l2ball_proximal_weights());
auto const result =
comm.all_reduce<int8_t>(residual_norm < padmm->residual_tolerance(), MPI_LAND);
#endif
SOPT_LOW_LOG(" - [PADMM] Residuals: {} <? {}", residual_norm, padmm->residual_tolerance());
return result;
});
padmm->objective_convergence([padmm_weak, conv, comm](Vector<t_complex> const &x,
Vector<t_complex> const &) mutable -> bool {
auto const padmm = padmm_weak.lock();
#if PURIFY_PADMM_ALGORITHM == 2
return conv(sopt::mpi::l1_norm(padmm->Psi().adjoint() * x, padmm->l1_proximal_weights(), comm));
#elif PURIFY_PADMM_ALGORITHM == 3 || PURIFY_PADMM_ALGORITHM == 1
return comm.all_reduce<uint8_t>(
conv(sopt::l1_norm(padmm->Psi().adjoint() * x, padmm->l1_proximal_weights())), MPI_LAND);
#endif
});
return padmm;
}
int main(int nargs, char const **args) {
sopt::logging::set_level("debug");
purify::logging::set_level("debug");
auto const session = sopt::mpi::init(nargs, args);
auto const world = sopt::mpi::Communicator::World();
const t_real FoV = 1; // deg
const t_real max_w = 100; // lambda
const std::string name = "M31";
const t_real snr = 30;
auto const kernel = "kb";
const bool w_term = true;
// string of fits file of image to reconstruct
auto ground_truth_image = pfitsio::read2d(image_filename(name + ".fits"));
ground_truth_image /= ground_truth_image.array().abs().maxCoeff();
const t_real cellsize = FoV / ground_truth_image.cols() * 60. * 60.;
// determine amount of visibilities to simulate
t_int const number_of_pixels = ground_truth_image.size();
t_int const number_of_vis = std::floor(number_of_pixels * 0.1);
// Generating random uv(w) coverage
auto const data = dirty_visibilities(ground_truth_image, number_of_vis, snr,
std::make_tuple(w_term, cellsize), world);
#if PURIFY_PADMM_ALGORITHM == 2 || PURIFY_PADMM_ALGORITHM == 3
#ifndef PURIFY_GPU
auto const measurements = std::get<2>(sopt::algorithm::normalise_operator<Vector<t_complex>>(
measurementoperator::init_degrid_operator_2d<Vector<t_complex>>(
world, std::get<0>(data), ground_truth_image.rows(), ground_truth_image.cols(), cellsize,
cellsize, 2, kernels::kernel_from_string.at(kernel), 8, 8, w_term),
100, 1e-4,
world.broadcast(
Vector<t_complex>::Random(ground_truth_image.rows() * ground_truth_image.cols())
.eval())));
#else
af::setDevice(0);
auto const measurements = std::get<2>(sopt::algorithm::normalise_operator<Vector<t_complex>>(
gpu::measurementoperator::init_degrid_operator_2d(
world, std::get<0>(data), ground_truth_image.rows(), ground_truth_image.cols(), cellsize,
cellsize, 2, kernels::kernel_from_string.at(kernel), 8, 8, w_term),
100, 1e-4,
world.broadcast(
Vector<t_complex>::Random(ground_truth_image.rows() * ground_truth_image.cols())
.eval())));
#endif
#elif PURIFY_PADMM_ALGORITHM == 1
#ifndef PURIFY_GPU
auto const measurements = std::get<2>(sopt::algorithm::normalise_operator<Vector<t_complex>>(
measurementoperator::init_degrid_operator_2d_mpi<Vector<t_complex>>(
world, std::get<0>(data), ground_truth_image.rows(), ground_truth_image.cols(), cellsize,
cellsize, 2, kernels::kernel_from_string.at(kernel), 8, 8, w_term),
100, 1e-4,
world.broadcast(
Vector<t_complex>::Random(ground_truth_image.rows() * ground_truth_image.cols())
.eval())));
#else
af::setDevice(0);
auto const measurements = std::get<2>(sopt::algorithm::normalise_operator<Vector<t_complex>>(
gpu::measurementoperator::init_degrid_operator_2d_mpi(
world, std::get<0>(data), ground_truth_image.rows(), ground_truth_image.cols(), cellsize,
cellsize, 2, kernels::kernel_from_string.at(kernel), 8, 8, w_term),
100, 1e-4,
world.broadcast(
Vector<t_complex>::Random(ground_truth_image.rows() * ground_truth_image.cols())
.eval())));
#endif
#endif
auto const sara = sopt::wavelets::distribute_sara(
sopt::wavelets::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)},
world);
// Create the padmm solver
auto const padmm = padmm_factory(measurements, sara, ground_truth_image, std::get<0>(data),
std::get<1>(data), world);
// calls padmm
auto const diagnostic = (*padmm)();
// makes sure we set things up correctly
assert(diagnostic.x.size() == ground_truth_image.size());
assert(world.broadcast(diagnostic.x).isApprox(diagnostic.x));
// then writes stuff to files
auto const residual_image = (measurements->adjoint() * diagnostic.residual).real();
auto const dirty_image = (measurements->adjoint() * std::get<0>(data).vis).real();
if (world.is_root()) {
boost::filesystem::path const path(output_filename(name));
#if PURIFY_PADMM_ALGORITHM == 3
auto const pb_path = path / kernel / "local_epsilon_replicated_grids";
#elif PURIFY_PADMM_ALGORITHM == 2
auto const pb_path = path / kernel / "global_epsilon_replicated_grids";
#elif PURIFY_PADMM_ALGORITHM == 1
auto const pb_path = path / kernel / "local_epsilon_distributed_grids";
#else
#error Unknown or unimplemented algorithm
#endif
mkdir_recursive(pb_path);
pfitsio::write2d(ground_truth_image.real(), (path / "input.fits").native());
pfitsio::write2d(dirty_image, ground_truth_image.rows(), ground_truth_image.cols(),
(pb_path / "dirty.fits").native());
pfitsio::write2d(diagnostic.x.real(), ground_truth_image.rows(), ground_truth_image.cols(),
(pb_path / "solution.fits").native());
pfitsio::write2d(residual_image, ground_truth_image.rows(), ground_truth_image.cols(),
(pb_path / "residual.fits").native());
}
return 0;
}
|
