Skip to content


Repository files navigation

Sparse OPTimisation Library

build codecov DOI


SOPT is an open-source C++ package available under the license below. It performs Sparse OPTimisation using state-of-the-art convex optimisation algorithms. It solves a variety of sparse regularisation problems, including the Sparsity Averaging Reweighted Analysis (SARA) algorithm.

SOPT also has several MPI wrappers that can be adapted for computational distirbution of various linear operators and convex optimisation algorithms. Wavelet Operators with SOPT also support multi-threading through OpenMP.

SOPT is written in C++ primarily but also contains partial and prototyped Matlab implementations of various algorithms.

SOPT is largely provided to support the PURIFY package, a companion open-source code to perform radio interferometric imaging, also written by the authors of SOPT. For further background please see the reference section.

This documentation outlines the necessary and optional dependencies upon which SOPT should be built, before describing installation and testing details and Matlab support. Contributors, references and license information then follows.

Dependencies installation

SOPT is mostly written in C++17. Pre-requisites and dependencies are listed in following and minimal versions required are tested against Travis CI meaning that they come natively with OSX and the Ubuntu Trusty release. These are also the default ones fetched by CMake.

C++ minimal dependencies:

  • CMake v3.9.2 A free software that allows cross-platform compilation.
  • GCC v7.3.0 GNU compiler for C++.
  • OpenMP v4.8.4 (Trusty) - Optional - Speeds up some of the operations.
  • Eigen3 v3.4.0 (Trusty) Modern C++ linear algebra. Downloaded automatically if absent.
  • Catch2 v3.4.0 - Optional - A C++ unit-testing framework only needed for testing. Downloaded automatically if absent.
  • google/benchmark - Optional - A C++ micro-benchmarking framework only needed for benchmarks. Downloaded automatically if absent.
  • tiff v4.5.1 (Trusty) Tag Image File Format library - only installed if needed.

Installing and building SOPT

Using Conan v2 (recommended)

Conan is a C++ package manager that helps deal with most of the C++ dependencies as well as the SOPT installation:

  1. Once the mandatory dependencies are present, git clone from the GitHub repository:

    git clone
  2. Then, the program can be built using conan:

    cd /path/to/code
    mkdir build
    cd build
    conan install .. -of . --build missing
    conan build .. -of .

Things to note:

  • To install in directory INSTALL_FOLDER, add the following options to the conan build command:

    conan build .. -of INSTALL_FOLDER
  • CMake build options should be passed as options to conan install using the -o flag with a value on or off. Possible options are:

    • tests (default on)
    • benchmarks (default off)
    • examples (default on)
    • openmp (default off)
    • dompi (default off)
    • docs (default off)
    • coverage (default off)
    • onnxrt (default off)

For example, to build with both MPI and OpenMP on you would use

conan install .. -of . --build missing -o openmp=on -o dompi=on
conan build .. -of .

Using CMake

If the dependencies are already available on your system, you can also install SOPT manually like so

cd /path/to/code
mkdir build
cd build
cmake .. -DCMAKE_INSTALL_PREFIX=${PWD}/../local
make -j
make -j install

On MacOS, you can also install most of the dependencies with Homebrew e.g.

brew install libtensorflow eigen tiff catch2

Note that the ONNXruntime interface is currently only supported when compiling with Clang on MacOS, but not with g++

Conan tips

You can set commonly used options, choices of compilers etc. in a conan profile. You can list profiles available on your system using conan profile list and select the profile you want to use with conan install with conan install .. -pr my_profile. CMake build options can also be added to the profile under [options]. Here is an example of a conan profile for building with a homebrew installed gcc 11 on MacOS.



To check everything went all right, run the test suite:

cd /path/to/code/build
ctest .

Machine-learning models

Machine-learning models are supported via the ONNXruntime interface. Nearly all modern ML toolkits allow to export their trained models into the ONNXruntime format using Python.

Install translation packages e.g. using pip:

pip install onnx
pip install onnxscript

PyTorch models can be exported to ONNXruntime like so

import torch
torch_model = ... # PyTorch model based on torch.nn
torch_input = torch_input = torch.randn(256, 256) # model input tensor
                  'model_name.onnx',        # output file name
                  export_params=True,       # store trained param weights
                  opset_version=11,         # ONNX version to export the model to
                  do_constant_folding=True, # optmise using pre-computed constant nodes
                  dynamic_axes={'input'  : {0 : 'batch_size'},
                                'output' : {0 : 'batch_size'}})

Tensorflow models can be exported to ONNXruntime like so

python -m tf2onnx.convert
       --saved-model model_name.pb
       --output model_name.onnx
       --opset 11
       --inputs input0:0
       --extra_opset StatefulPartitionedCall:0

Unknown TF input dimensions can be specified e.g. using --inputs 'input0:0[1,256,256,1]'.

After the export, load the model and verify that it's well formed like so

import onnx
onnx_model = onnx.load("model_name.onnx")
print( onnx_model.graph.input )

Netron is a useful online tool to help visualise the model.


A separate Matlab implementation is provided with SOPT. This implementation includes some (but not all) of the optimisation algorithms implemented in the C++ code, including the SARA algorithm.

The Matlab implementation is contained in the matlab directory. This is a stand-alone implementation and does not call any of the C++ code. In future, Matlab interfaces to the C++ code may also be included in SOPT.

See matlab/README.txt for an overview of the Matlab implementation. The stand-alone Matlab implementation is also self-documenting; corresponding documentation can be found in matlab/doc. We thank Gilles Puy for contributing to this Matlab implementation.


Check the [contributors](@ref sopt_contributors) page (github).

References and citation

If you use SOPT for work that results in publication, please reference the webpage and our related academic papers:

  1. L. Pratley et al. (to be published)
  2. A. Onose, R. E. Carrillo, A. Repetti, J. D. McEwen, J.-P. Thiran, J.-C. Pesquet, and Y. Wiaux. "Scalable splitting algorithms for big-data interferometric imaging in the SKA era" Mon. Not. Roy. Astron. Soc. 462(4):4314-4335 (2016) arXiv:1601.04026
  3. R. E. Carrillo, J. D. McEwen, D. Van De Ville, J.-P. Thiran, and Y. Wiaux. "Sparsity averaging for compressive imaging" IEEE Signal Processing Letters 20(6):591-594 (2013) arXiv:1208.2330
  4. R. E. Carrillo, J. D. McEwen and Y. Wiaux. "Sparsity Averaging Reweighted Analysis (SARA): a novel algorithm for radio-interferometric imaging" Mon. Not. Roy. Astron. Soc. 426(2):1223-1234 (2012) arXiv:1205.3123


SOPT: Sparse OPTimisation package Copyright (C) 2013-2024

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details (LICENSE.txt).

You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.



For any questions or comments, feel free to contact Jason McEwen, or add an issue to the issue tracker.


The code is given for educational purpose. For the Matlab version of the code see the folder matlab.