Sparse OPTimisation
Sparse OPTimisation Library

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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++11. 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++.
  • UCL/GreatCMakeCookOff Collection of CMake recipes. Downloaded automatically if absent.
  • OpenMP v4.8.4 (Trusty) - Optional - Speeds up some of the operations.
  • Conan - C++ package manager which installs the following:
    • Eigen3 v3.2.0 (Trusty) Modern C++ linear algebra. Downloaded automatically if absent.
    • spdlog v* - Optional - Logging library. Downloaded automatically if absent.
    • Catch2 v2.2.3 - 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 v4.0.3 (Trusty) Tag Image File Format library - only installed if needed.

Installing and building SOPT

You can build SOPT entirely from the source code. Once the mandatory dependencies are present, git clone from the GitHub repository:

git clone

Then, the program can be built with standard CMake command:

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

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

conan build .. -bf INSTALL_FOLDER -if .

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)
  • logging (default on)
  • openmp (default on)
  • mpi (default on)
  • docs (default off)
  • coverage (default off)

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

conan install .. --build missing -o openmp=off -o mpi=off
conan build ..

Common errors

If you are using the g++ compiler and get an error to do with the package spdlog, try adding the option -s compiler.libcxx=libstdc++11 to the conan build command. This option is also necessary when building with gcc on MacOS.

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 .


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 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) 2013-2019

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.