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// SPDX-License-Identifier: LGPL-3.0-only
#include "parallel_deconvolution.h"
#include <algorithm>
#include <memory>
#include <sstream>
#include <aocommon/dynamicfor.h>
#include <aocommon/units/fluxdensity.h>
#include <schaapcommon/math/convolution.h>
#include "algorithms/multiscale_algorithm.h"
#include "math/dijkstra_splitter.h"
using aocommon::Image;
using aocommon::Logger;
namespace radler::algorithms {
namespace {
/**
* Returns the nearest PSF to a selected position.
*
* When the distance is equal for multiple positions the index to the first
* PSF in the input is returned.
*
* @note When @a psf_offsets is empty the first index is returned. This happens
* when no direction-dependent PSFs are used, in that case there's always one
* PSF.
*/
size_t NearestPsfIndex(const std::vector<PsfOffset>& psf_offsets, size_t x,
size_t y) noexcept {
if (psf_offsets.empty()) {
return 0;
}
// Calculates the squared distance between a psf_offset and the position x, y.
// Note comparing squared distances is the same as comparing the real
// distance.
auto distance = [x, y](const PsfOffset& psf_offset) {
ssize_t delta_x = psf_offset.x - x;
ssize_t delta_y = psf_offset.y - y;
return size_t(delta_x * delta_x) + size_t(delta_y * delta_y);
};
return std::min_element(
psf_offsets.begin(), psf_offsets.end(),
[&distance](const PsfOffset& lhs, const PsfOffset& rhs) {
return distance(lhs) < distance(rhs);
}) -
psf_offsets.begin();
}
/**
* Calculate how to split the full image into sub-images and make these
* sub-images. Also makes the masks belonging to the sub-images. Even when there
* is no full-size mask, the sub-images will have a mask that delineates the
* boundary to make sure that every pixel is only active in one sub-image.
* @param image Integrated image that is used to calculate the "minimum
* power"-path for splitting.
* @param mask Full size mask or nullptr if there is no mask. The sub-image
* masks are the combination of this mask and the boundary mask.
* @param [out] psf_image_indices used to store the indices to the nearest psf
* images for all subimages. Should be empty on input.
*/
std::vector<SubImage> MakeSubImages(const Image& image, const bool* mask,
const std::vector<PsfOffset>& psf_offsets,
const Settings& settings,
std::vector<size_t>& psf_image_indices) {
assert(psf_image_indices.empty());
const size_t width = image.Width();
const size_t height = image.Height();
const size_t avgHSubImageSize = width / settings.parallel.grid_width;
const size_t avgVSubImageSize = height / settings.parallel.grid_height;
Image dividingLine(width, height, 0.0);
aocommon::UVector<bool> largeScratchMask(width * height);
math::DijkstraSplitter divisor(width, height);
struct VerticalArea {
aocommon::UVector<bool> mask;
size_t x, width;
};
std::vector<VerticalArea> verticalAreas(settings.parallel.grid_width);
Logger::Info << "Calculating edge paths...\n";
aocommon::DynamicFor<size_t> splitLoop;
// Divide into columns (i.e. construct the vertical lines)
splitLoop.Run(1, settings.parallel.grid_width, [&](size_t divNr) {
const size_t splitMiddle = width * divNr / settings.parallel.grid_width;
const size_t splitStart = splitMiddle - avgHSubImageSize / 4;
const size_t splitEnd = splitMiddle + avgHSubImageSize / 4;
divisor.DivideVertically(image.Data(), dividingLine.Data(), splitStart,
splitEnd);
});
for (size_t divNr = 0; divNr != settings.parallel.grid_width; ++divNr) {
const size_t midX =
divNr * width / settings.parallel.grid_width + avgHSubImageSize / 2;
VerticalArea& area = verticalAreas[divNr];
divisor.FloodVerticalArea(dividingLine.Data(), midX,
largeScratchMask.data(), area.x, area.width);
area.mask.resize(area.width * height);
Image::TrimBox(area.mask.data(), area.x, 0, area.width, height,
largeScratchMask.data(), width, height);
}
// Make the rows (horizontal lines)
dividingLine = 0.0f;
splitLoop.Run(1, settings.parallel.grid_height, [&](size_t divNr) {
const size_t splitMiddle = height * divNr / settings.parallel.grid_height;
const size_t splitStart = splitMiddle - avgVSubImageSize / 4;
const size_t splitEnd = splitMiddle + avgVSubImageSize / 4;
divisor.DivideHorizontally(image.Data(), dividingLine.Data(), splitStart,
splitEnd);
});
Logger::Info << "Calculating bounding boxes and submasks...\n";
// Find the bounding boxes and clean masks for each subimage
aocommon::UVector<bool> bounding_mask(width * height);
std::vector<SubImage> subImages;
for (size_t y = 0; y != settings.parallel.grid_height; ++y) {
const size_t midY =
y * height / settings.parallel.grid_height + avgVSubImageSize / 2;
size_t hAreaY, hAreaWidth;
divisor.FloodHorizontalArea(dividingLine.Data(), midY,
largeScratchMask.data(), hAreaY, hAreaWidth);
for (size_t x = 0; x != settings.parallel.grid_width; ++x) {
subImages.emplace_back();
SubImage& subImage = subImages.back();
subImage.index = subImages.size() - 1;
const VerticalArea& vArea = verticalAreas[x];
divisor.GetBoundingMask(vArea.mask.data(), vArea.x, vArea.width,
largeScratchMask.data(), bounding_mask.data(),
subImage.x, subImage.y, subImage.width,
subImage.height);
Logger::Debug << "Subimage " << subImages.size() << " at (" << subImage.x
<< "," << subImage.y << ") - ("
<< subImage.x + subImage.width << ","
<< subImage.y + subImage.height << ")\n";
subImage.mask.resize(subImage.width * subImage.height);
Image::TrimBox(subImage.mask.data(), subImage.x, subImage.y,
subImage.width, subImage.height, bounding_mask.data(),
width, height);
subImage.boundary_mask = subImage.mask;
// If a user mask is active, take the union of that mask with the boundary
// mask (note that 'mask' is reused as a scratch space)
if (mask != nullptr) {
Image::TrimBox(bounding_mask.data(), subImage.x, subImage.y,
subImage.width, subImage.height, mask, width, height);
for (size_t i = 0; i != subImage.mask.size(); ++i) {
subImage.mask[i] = subImage.mask[i] && bounding_mask[i];
}
}
psf_image_indices.emplace_back(
NearestPsfIndex(psf_offsets, subImage.x + subImage.width / 2,
subImage.y + subImage.height / 2));
}
}
return subImages;
}
} // namespace
ParallelDeconvolution::ParallelDeconvolution(const Settings& settings)
: settings_(settings),
mask_(nullptr),
track_per_scale_masks_(false),
use_per_scale_masks_(false) {
// Make all FFTWF plan calls inside ParallelDeconvolution
// thread safe.
schaapcommon::math::MakeFftwfPlannerThreadSafe();
}
ParallelDeconvolution::~ParallelDeconvolution() = default;
ComponentList ParallelDeconvolution::GetComponentList(
const WorkTable& table) const {
// TODO make this work with subimages
ComponentList list;
if (settings_.algorithm_type == AlgorithmType::kMultiscale) {
// If no parallel deconvolution was used, the component list must be
// retrieved from the deconvolution algorithm.
if (algorithms_.size() == 1) {
list = static_cast<MultiScaleAlgorithm*>(algorithms_.front().get())
->GetComponentList();
} else {
list = *component_list_;
}
} else {
const size_t w = settings_.trimmed_image_width;
const size_t h = settings_.trimmed_image_height;
ImageSet modelSet(table, settings_.squared_joins,
settings_.linked_polarizations, w, h);
modelSet.LoadAndAverage(false);
list = ComponentList(w, h, modelSet);
}
list.MergeDuplicates();
return list;
}
const DeconvolutionAlgorithm& ParallelDeconvolution::MaxScaleCountAlgorithm()
const {
if (settings_.algorithm_type == AlgorithmType::kMultiscale) {
MultiScaleAlgorithm* maxAlgorithm =
static_cast<MultiScaleAlgorithm*>(algorithms_.front().get());
for (size_t i = 1; i != algorithms_.size(); ++i) {
MultiScaleAlgorithm* mAlg =
static_cast<MultiScaleAlgorithm*>(algorithms_[i].get());
if (mAlg->ScaleCount() > maxAlgorithm->ScaleCount()) {
maxAlgorithm = mAlg;
}
}
return *maxAlgorithm;
} else {
return FirstAlgorithm();
}
}
void ParallelDeconvolution::SetAlgorithm(
std::unique_ptr<DeconvolutionAlgorithm> algorithm) {
algorithms_.resize(settings_.parallel.grid_width *
settings_.parallel.grid_height);
algorithms_.front() = std::move(algorithm);
const size_t parallel_subimages =
std::min(settings_.parallel.max_threads, algorithms_.size());
const size_t threads_per_alg =
(settings_.thread_count + parallel_subimages - 1) / parallel_subimages;
Logger::Debug << "Parallel deconvolution will use " << algorithms_.size()
<< " subimages, each using " << threads_per_alg
<< " threads.\n";
for (size_t i = 1; i != algorithms_.size(); ++i) {
algorithms_[i] = algorithms_.front()->Clone();
}
}
void ParallelDeconvolution::SetRmsFactorImage(Image&& image) {
if (algorithms_.size() == 1) {
algorithms_.front()->SetRmsFactorImage(std::move(image));
} else {
rms_image_ = std::move(image);
}
}
void ParallelDeconvolution::SetThreshold(double threshold) {
for (auto& alg : algorithms_) alg->SetThreshold(threshold);
}
void ParallelDeconvolution::SetAutoMaskMode(bool track_per_scale_masks,
bool use_per_scale_masks) {
track_per_scale_masks_ = track_per_scale_masks;
use_per_scale_masks_ = use_per_scale_masks;
for (auto& alg : algorithms_) {
class MultiScaleAlgorithm& algorithm =
static_cast<class MultiScaleAlgorithm&>(*alg);
algorithm.SetAutoMaskMode(track_per_scale_masks, use_per_scale_masks);
}
}
void ParallelDeconvolution::SetCleanMask(const bool* mask) {
if (algorithms_.size() == 1) {
algorithms_.front()->SetCleanMask(mask);
} else {
mask_ = mask;
}
}
void ParallelDeconvolution::SetSpectrallyForcedImages(
std::vector<Image>&& images) {
if (algorithms_.size() == 1) {
algorithms_.front()->SetSpectrallyForcedImages(std::move(images));
} else {
spectrally_forced_images_ = std::move(images);
}
}
void ParallelDeconvolution::RunSubImage(
SubImage& sub_image, ImageSet& data_image, const ImageSet& model_image,
ImageSet& result_model, const std::vector<aocommon::Image>& psf_images,
double major_iteration_threshold, bool find_peak_only, std::mutex& mutex) {
const size_t width = settings_.trimmed_image_width;
const size_t height = settings_.trimmed_image_height;
std::unique_ptr<ImageSet> sub_model;
std::unique_ptr<ImageSet> sub_data;
{
const std::lock_guard<std::mutex> lock(mutex);
sub_data =
data_image.Trim(sub_image.x, sub_image.y, sub_image.x + sub_image.width,
sub_image.y + sub_image.height, width);
// Because the model of this subimage might extend outside of its boundaries
// (because of multiscale components), the model is placed back on the image
// by adding its values. This requires that values outside the boundary are
// set to zero at this point (before continuing deconvolution), otherwise
// multiple subimages could add the same sources.
sub_model = model_image.TrimMasked(
sub_image.x, sub_image.y, sub_image.x + sub_image.width,
sub_image.y + sub_image.height, width, sub_image.boundary_mask.data());
}
// Make a copy of the images at the start to be able to undo the results of
// deconvolution if it diverges.
std::vector<aocommon::Image> initial_model_images = sub_model->Images();
// Construct the smaller psfs
std::vector<Image> sub_psfs;
sub_psfs.reserve(psf_images.size());
for (const aocommon::Image& psf_image : psf_images) {
// The PSF is smaller than the sub image when using a fine grained
// direction-dependent(DD) PSF grid. It is larger than the subimage when
// using a coarse grained DD PSF grid. Resize supports both cases.
sub_psfs.emplace_back(psf_image.Resize(sub_image.width, sub_image.height));
}
algorithms_[sub_image.index]->SetCleanMask(sub_image.mask.data());
// Construct smaller RMS image if necessary
if (!rms_image_.Empty()) {
Image sub_rms_image = rms_image_.TrimBox(sub_image.x, sub_image.y,
sub_image.width, sub_image.height);
algorithms_[sub_image.index]->SetRmsFactorImage(std::move(sub_rms_image));
}
// If a forced spectral image is active, trim it to the subimage size
if (!spectrally_forced_images_.empty()) {
std::vector<Image> sub_spectral_images(spectrally_forced_images_.size());
for (size_t i = 0; i != spectrally_forced_images_.size(); ++i) {
sub_spectral_images[i] = spectrally_forced_images_[i].TrimBox(
sub_image.x, sub_image.y, sub_image.width, sub_image.height);
}
algorithms_[sub_image.index]->SetSpectrallyForcedImages(
std::move(sub_spectral_images));
}
const size_t max_n_iter = algorithms_[sub_image.index]->MaxIterations();
if (find_peak_only) {
algorithms_[sub_image.index]->SetMaxIterations(0);
} else {
algorithms_[sub_image.index]->SetMajorIterationThreshold(
major_iteration_threshold);
}
if (use_per_scale_masks_ || track_per_scale_masks_) {
const std::lock_guard<std::mutex> lock(mutex);
MultiScaleAlgorithm& multi_scale_algorithm =
static_cast<class MultiScaleAlgorithm&>(*algorithms_[sub_image.index]);
// During the first iteration, multi_scale_algorithm will not have
// scales/masks yet and the nr scales has also not been determined yet.
if (!scale_masks_.empty()) {
// Here we set the scale mask for the multiscale algorithm.
// The maximum number of scales in the previous iteration can be found by
// scale_masks_.size(). Not all multi_scale_algorithms might have used
// that many scales, so we have to take this into account
multi_scale_algorithm.SetScaleMaskCount(std::max(
multi_scale_algorithm.GetScaleMaskCount(), scale_masks_.size()));
for (size_t i = 0; i != multi_scale_algorithm.GetScaleMaskCount(); ++i) {
aocommon::UVector<bool>& scale_mask =
multi_scale_algorithm.GetScaleMask(i);
scale_mask.assign(sub_image.width * sub_image.height, false);
if (i < scale_masks_.size()) {
scale_masks_[i].GetBox(scale_mask.data(), sub_image.x, sub_image.y,
sub_image.width, sub_image.height);
// If the scale-independent mask is set, we'll have to take the
// intersection between that mask and the scale mask. Values in the
// scale dependent mask may be true values that fall outside the
// boundary, hence they should not be cleaned. Multiscale ignores the
// scale-independent mask when scale masks are set.
for (size_t i = 0; i != scale_mask.size(); ++i) {
scale_mask[i] = scale_mask[i] && sub_image.mask[i];
}
}
}
}
}
const double peak_at_start = std::fabs(sub_image.peak);
const DeconvolutionResult result =
algorithms_[sub_image.index]->ExecuteMajorIteration(*sub_data, *sub_model,
sub_psfs);
sub_image.peak = result.final_peak_value;
sub_image.reached_major_threshold = result.another_iteration_required;
// When diverging, a warning is displayed and the results of this sub-image
// are not written back to the full image.
const bool converging = (settings_.divergence_limit == 0.0 ||
std::fabs(sub_image.peak) <=
peak_at_start * settings_.divergence_limit) &&
std::isfinite(sub_image.peak) && !result.is_diverging;
if (!converging && !find_peak_only) {
std::ostringstream warning_str;
warning_str << "Peak of sub-image " << sub_image.index << " increased from "
<< aocommon::units::FluxDensity::ToNiceString(peak_at_start)
<< " to "
<< aocommon::units::FluxDensity::ToNiceString(sub_image.peak)
<< " and deconvolution probably diverged: resetting.\n";
aocommon::Logger::Warn << warning_str.str();
// As we are diverging, this sub-image should not cause a new major
// iteration
sub_image.reached_major_threshold = false;
}
// Since this was an RMS image specifically for this subimage size, we free it
// immediately
algorithms_[sub_image.index]->SetRmsFactorImage(Image());
if (track_per_scale_masks_ && converging && !find_peak_only) {
const std::lock_guard<std::mutex> lock(mutex);
MultiScaleAlgorithm& multi_scale_algorithm =
static_cast<class MultiScaleAlgorithm&>(*algorithms_[sub_image.index]);
if (scale_masks_.empty()) {
scale_masks_.reserve(multi_scale_algorithm.ScaleCount());
for (size_t i = 0; i != multi_scale_algorithm.ScaleCount(); ++i) {
scale_masks_.emplace_back(width, height);
}
}
Logger::Debug << "Compressing scale-dependent masks...\n";
for (size_t scale_index = 0;
scale_index != multi_scale_algorithm.ScaleCount(); ++scale_index) {
const aocommon::UVector<bool>& ms_mask =
multi_scale_algorithm.GetScaleMask(scale_index);
if (scale_index < scale_masks_.size()) {
aocommon::UVector<bool> combined_mask(sub_image.width *
sub_image.height);
scale_masks_[scale_index].GetBox(combined_mask.data(), sub_image.x,
sub_image.y, sub_image.width,
sub_image.height);
for (size_t pixel = 0; pixel != combined_mask.size(); ++pixel) {
if (sub_image.boundary_mask[pixel]) {
combined_mask[pixel] = ms_mask[pixel];
}
}
scale_masks_[scale_index].SetBox(combined_mask.data(), sub_image.x,
sub_image.y, sub_image.width,
sub_image.height);
std::stringstream compression_rate;
compression_rate << std::fixed << std::setprecision(1)
<< width * height /
scale_masks_[scale_index].CompressedSize();
Logger::Debug << std::fixed << std::setprecision(1);
Logger::Debug << "Compression rate of scale mask " << scale_index
<< ": " << compression_rate.str() << "x\n";
}
}
}
if (settings_.save_source_list &&
settings_.algorithm_type == AlgorithmType::kMultiscale) {
MultiScaleAlgorithm& algorithm =
static_cast<MultiScaleAlgorithm&>(*algorithms_[sub_image.index]);
if (converging) {
const std::lock_guard<std::mutex> lock(mutex);
if (!component_list_) {
component_list_ = std::make_unique<ComponentList>(
width, height, algorithm.ScaleCount(), data_image.Size());
}
component_list_->Add(algorithm.GetComponentList(), sub_image.x,
sub_image.y);
}
algorithm.ClearComponentList();
}
if (find_peak_only) {
algorithms_[sub_image.index]->SetMaxIterations(max_n_iter);
} else {
if (converging) {
const std::lock_guard<std::mutex> lock(mutex);
data_image.CopyMasked(*sub_data, sub_image.x, sub_image.y,
sub_image.boundary_mask.data());
} else {
// The result model starts empty. Even when diverging, the model
// as it was before this iteration should be added to it.
sub_model->SetImages(std::move(initial_model_images));
}
result_model.AddSubImage(*sub_model, sub_image.x, sub_image.y);
}
}
void ParallelDeconvolution::ExecuteMajorIteration(
ImageSet& data_image, ImageSet& model_image,
const std::vector<std::vector<aocommon::Image>>& psf_images,
const std::vector<PsfOffset>& psf_offsets, bool& reached_major_threshold) {
if (algorithms_.size() == 1) {
ExecuteSingleThreadedRun(data_image, model_image, psf_images, psf_offsets,
reached_major_threshold);
} else {
ExecuteParallelRun(data_image, model_image, psf_images, psf_offsets,
reached_major_threshold);
}
}
void ParallelDeconvolution::ExecuteSingleThreadedRun(
ImageSet& data_image, ImageSet& model_image,
const std::vector<std::vector<aocommon::Image>>& psf_images,
const std::vector<PsfOffset>& psf_offsets, bool& reached_major_threshold) {
DeconvolutionAlgorithm& algorithm = *algorithms_.front();
// The index of the nearest direction-dependent PSF, or the first when no
// direction-dependent PSFs are used.
const size_t psf_image_index = NearestPsfIndex(
psf_offsets, model_image.Width() / 2, model_image.Height() / 2);
aocommon::ForwardingLogReceiver fwdReceiver;
algorithm.SetLogReceiver(fwdReceiver);
// When using direction-dependent PSFs, the PSFs may have a different size.
// All PSF images for a psf_image_index should have equal sizes.
const aocommon::Image& first_psf_image = psf_images[psf_image_index].front();
const bool resize_psfs = first_psf_image.Width() != data_image.Width() ||
first_psf_image.Height() != data_image.Height();
if (!resize_psfs) {
const DeconvolutionResult result = algorithm.ExecuteMajorIteration(
data_image, model_image, psf_images[psf_image_index]);
reached_major_threshold = result.another_iteration_required;
} else {
// When using direction-dependent PSFs, the PSFs can only be smaller.
assert(first_psf_image.Width() <= data_image.Width());
assert(first_psf_image.Height() <= data_image.Height());
std::vector<aocommon::Image> resized_psf_images;
resized_psf_images.reserve(psf_images[psf_image_index].size());
for (const aocommon::Image& psf_image : psf_images[psf_image_index]) {
resized_psf_images.push_back(
psf_image.Untrim(data_image.Width(), data_image.Height()));
}
const DeconvolutionResult result = algorithm.ExecuteMajorIteration(
data_image, model_image, resized_psf_images);
reached_major_threshold = result.another_iteration_required;
}
}
void ParallelDeconvolution::ExecuteParallelRun(
ImageSet& data_image, ImageSet& model_image,
const std::vector<std::vector<aocommon::Image>>& psf_images,
const std::vector<PsfOffset>& psf_offsets, bool& reached_major_threshold) {
const size_t width = data_image.Width();
const size_t height = data_image.Height();
Image image(width, height);
data_image.GetLinearIntegrated(image);
// The index with the nearest psf_images for all subimages.
std::vector<size_t> psf_image_indices;
std::vector<SubImage> subImages =
MakeSubImages(image, mask_, psf_offsets, settings_, psf_image_indices);
// Initialize loggers
std::mutex mutex;
logs_.Initialize(settings_.parallel.grid_width,
settings_.parallel.grid_height);
for (size_t i = 0; i != algorithms_.size(); ++i) {
algorithms_[i]->SetLogReceiver(logs_[i]);
}
// Find the starting peak over all subimages
ImageSet resultModel(model_image, model_image.Width(), model_image.Height());
resultModel = 0.0;
aocommon::RecursiveFor::NestedRun(0, algorithms_.size(), [&](size_t index) {
logs_.Activate(index);
RunSubImage(subImages[index], data_image, model_image, resultModel,
psf_images[psf_image_indices[index]], 0.0, true, mutex);
logs_.Deactivate(index);
logs_[index].Mute(false);
logs_[index].Info << "Sub-image " << index << " returned peak position.\n";
logs_[index].Mute(true);
});
double maxValue = 0.0;
size_t indexOfMax = 0;
for (const SubImage& img : subImages) {
if (img.peak > maxValue) {
maxValue = img.peak;
indexOfMax = img.index;
}
}
Logger::Info << "Subimage " << (indexOfMax + 1) << " has maximum peak of "
<< aocommon::units::FluxDensity::ToNiceString(maxValue) << ".\n";
double mIterThreshold = maxValue * (1.0 - settings_.major_loop_gain);
// Run the deconvolution
aocommon::RecursiveFor::NestedRun(0, algorithms_.size(), [&](size_t index) {
logs_.Activate(index);
RunSubImage(subImages[index], data_image, model_image, resultModel,
psf_images[psf_image_indices[index]], mIterThreshold, false,
mutex);
logs_.Deactivate(index);
logs_[index].Mute(false);
logs_[index].Info << "Sub-image " << index
<< " finished its deconvolution iteration.\n";
logs_[index].Mute(true);
});
model_image.SetImages(std::move(resultModel));
rms_image_.Reset();
size_t subImagesFinished = 0;
reached_major_threshold = false;
bool reachedMaxNIter = false;
for (SubImage& img : subImages) {
if (!img.reached_major_threshold) ++subImagesFinished;
if (algorithms_[img.index]->IterationNumber() >=
algorithms_[img.index]->MaxIterations()) {
reachedMaxNIter = true;
}
}
Logger::Info << subImagesFinished << " / " << subImages.size()
<< " sub-images finished";
reached_major_threshold = (subImagesFinished != subImages.size());
if (reached_major_threshold && !reachedMaxNIter) {
Logger::Info << ": Continue next major iteration.\n";
} else if (reached_major_threshold && reachedMaxNIter) {
Logger::Info << ", but nr. of iterations reached at least once: "
"Deconvolution finished.\n";
reached_major_threshold = false;
} else {
Logger::Info << ": Deconvolution finished.\n";
}
}
} // namespace radler::algorithms
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