adriaj / compositesps

CompositeSpS

This python repository provides the code accompanying the paper "A Decoupled Approach for Composite Sparse-plus-Smooth Penalized Optimization".

The optimization problem considered can be stated as follows:

{\arg\min}\ \frac{1}{2} ||\mathbf{y} - \mathbf{A}(\mathbf{x}_1 + \mathbf{x}_2)||_2^2 + \lambda_1 ||\mathbf{L}_1\mathbf{x}_1||_1 + \frac{\lambda_2}{2} ||\mathbf{L}_2\mathbf{x}_2||_2^2,

where the optimization variables are {\mathbf{x}_1, \mathbf{x}_2 \in \mathbb{R}^N}.

The code implements:

• a coupled method, that directly solves the problem above,
• a decoupled approach, that relies on a representer theorem presented in the companion article, that allows to solve two smaller dimensions problems.

We illustrate that, in the application case considered here, the decoupled approach leads to significant time speedups, while providing a reconstruction of similar or higher quality than the coupled method.

Installation

Instructions are provided in the src/howtoinstall.txt file.

$ git clone [email protected]:AdriaJ/CompositeSpS.git
$ cd CompositeSpS
$ conda create -n compsps python=3.10
$ conda activate compsps
$ conda install numpy matplotlib
$ pip install finufft
$ pip install pyxu==1.2.0
$ conda install jupyter

Description of the files

The folder src/ contains the code to simulate the optimization problem, including the simulation of the input composite signal and the sampling operator, as well as the numerical solvers, for both the coupled and decoupled methods.

The folder scripts/ provides the codes to reproduce the results displayed in the article, as well as other to experiment with the decoupled approach and play with the reconstruction parameters. Additionally, scripts are provided to plot the results in a handy and insightful manner.

Citation

For citing this package, please refer to the ArXiv preprint, until further notice of acceptance.

@misc{jarret2024composite,
    title={{A Decoupled Approach for Composite Sparse-plus-Smooth Penalized Optimization}},
    author={Jarret, Adrian and Costa, Valérie and Fageot, Julien},
    year={2024},
    eprint={todo},
    archivePrefix={arXiv},
    primaryClass={todo}
}