Low-Rank Approximation Tutorial

Description

The objective is to provide a beginner level introduction to the concept of low-rank approximation, in particular as a regularisation method for solving linear inverse problems. The tutorial does not provide an in-depth mathematical background nor detailed explanations for every topic. Tutees should supplement this tutorial with further reading of the various references provided in the notebooks for a more comprehensive understanding of the subject. More information about how cutting-edge sparsity techniques are being applied to astrophysical data is available on the CosmoStat website.

This tutorial is comprised of a Jupyter notebook that demonstrate how the low-rank approximation works as well as showing the applicability of this tools to various simple problems.

All code blocks are provided in Python (support for >=3.5) and the number of external packages required to run the examples has be kept to a minimum. All of the code has been clearly presented inside the notebook at least once to avoid the use of any “black boxes” for solving the problems presented.

Contents

• Requirements
• Notebooks
• Acknowledgements

Requirements

In order to run the tutorial notebooks tutees will need to have the following installed:

• Python (require >=3.5)
• NumPy (recommend >=1.16.2)
• SciPy (recommend >=1.2.1)
• Astropy (recommend >=3.1.2)
• Matplotlib (recommend >=3.0.3)
• Jupyter (recommend >=1.0.0)

All of the packages listed above can easily be installed using either pip or Anaconda.

e.g.

$ pip install numpy scipy astropy matplotlib jupyter

or

$ conda install numpy scipy astropy matplotlib jupyter

Notebooks

1. Introduction to Low-Rank Approximation

Acknowledgements

S. Farrens would like to acknowledge the following people for helpful feedback and ideas for producing this tutorial: Fred Ngolè-Mboula.