Pynopt

Simple numpy implementations for some non-smooth, non-convex optimisation problems arising in data processing, such as

• compressed sensing
• matrix completion/sensing
• robust low-rank estimation (Robust PCA)

The goal is to write a algorithms for a unified treatment of the above to be used in a number of applications, such as video seperation, multispectral imaging, exoplanet detection, image inpainting, and others.

Problem classes

LinearProblem

Solve

$$ \min_{x} \big\lVert A(x) - b \big\rVert_2\qquad \mathrm{s.t.}\quad x \in C$$

where $C$ can be a sparse set or a fixed rank set, and $A$ is a linear operator from pylops or scipy's LinearOperator class.

Solvers: NIHT

LinearProblemSum

Solve the linear combination

$$ \min_{x_i} \big\lVert A_1(x_1) + A_2(x_2) - b \big\rVert_2\qquad \mathrm{s.t.}\quad x_i \in C_i$$

Solvers: NAHT

Requirements

• numpy (1.21.3)
• pandas (1.3.4)
• scikit-learn (1.0.1)

Citation

@article{Tanner2023Compressed,
    title = {Compressed sensing of low-rank plus sparse matrices},
    author = {Jared Tanner and Simon Vary},
    journal = {Applied and Computational Harmonic Analysis},
    volume = {64},
    pages = {254-293},
    year = {2023},
    issn = {1063-5203},
    doi = {https://doi.org/10.1016/j.acha.2023.01.008},
    url = {https://www.sciencedirect.com/science/article/pii/S106352032300009X}
}