add README

Author: Christian Kümmerle

README.md

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+
+# Recovering Simultaneously Structured Data via Non-Convex Iteratively Reweighted Least Squares - SimIRLS
+
+[Christian Kümmerle](http://ckuemmerle.com) and [Johannes Maly](https://johannes-maly.github.io)
+
+This repository contains the code for the *NeurIPS 2023* paper [*Recovering Simultaneously Structured Data via Non-Convex Iteratively Reweighted Least Squares*](https://openreview.net/pdf?id=50hs53Zb3w) [[KM23]](#KM23), which studies an iteratively reweighted least squares approach (`IRLS` or `IRLS-LRRS`) based on a smoothing strategy and a non-convex surrogate modelling for the problem of recovering simultaneously low-rank and row-sparse matrices from linear masureuments.
+
+[[arXiv]](https://arxiv.org/pdf/2306.04961.pdf) [[Paper at OpenReview]](https://openreview.net/pdf?id=50hs53Zb3w)
+
+Reproducibile experiments and algorithmic implementations are provided in MATLAB. 
+
+### Citation
+Please cite this work as:
+
+```
+@inproceedings{KuemmerleMaly2023,
+ title = {Recovering Simultaneously Structured Data via Non-Convex Iteratively Reweighted Least Squares},
+ author = {K{\"u}mmerle, Christian and Maly, Johannes},
+ booktitle = {Advances in Neural Information Processing Systems (NeurIPS 2023)},
+ volume = {36},
+ year = {2023}
+}
+
+```
+
+## Installation
+   
+1. Obtain files of repository via either:
+  -  Clone repository via `git clone --recurse-submodules https://github.com/ckuemmerle/simirls.git` (note the flag `--recurse-submodules` due to usage of submodule [riemannian_thresholding](https://github.com/ckuemmerle/riemannian_thresholding)))
+  -  Download files and unpack into your MATLAB path, then download [riemannian_thresholding](https://github.com/ckuemmerle/riemannian_thresholding) and unpack into `/algorithms/riemannian_thresholding`.  
+2. Run `setup.m` from main folder of repository as current MATLAB folder.
+
+## Usage
+* `demo_LRRS_Gaussian_rank1_IRLS`: Minimal example of how to use `IRLS-LRRS` [[KM23]](#KM23) to solve a randomly generated simultaneous low-rank and row-sparse recovery problem (Gaussian measurements).
+* `demo_LRRS_Gaussian_rank1`: Also runs `SPF` [[LWB18]](#LWB18) and `RiemAdaIHT` [[EKPU23]](#EKPU23) alongside of `IRLS-LRRS` for problem above.
+* `run_single_Example_LRRS`: Run to choose one of the problem setups of folder `/Examples/` via text input. Use repository's main folder as current folder when doing this.
+
+### Subfolders
+* `/Examples`: Contains files to define the parameters various example problem setups.
+* `/algorithms`: Contains algorithm implementations
+* `/experiment_setup`: Code to setup and run experiments
+* `/experiments`: Scripts to load data and reproduce experiments of Figures 1-7 in [[KM23]](#KM23)
+* `/results`: Plots containing experimental results of Figures 1-7 of [[KM23]](#KM23)
+* `/utilities`: Contains various helper functions
+
+Please contact the authors [[KM23]](#KM23) for access to the original data for phase transitions experiments of Figure 1-2, 4-5 in [[KM23]](#KM23).
+
+## List of algorithms
+* `IRLS` (or `IRLS-LRRS`): *Iteratively Reweighted Least Squares (for Low-Rank and Row-Sparse recovery)*, Algorithm 1 of [[KM23]](#KM23).
+* `SPF`: *Sparse Power Factorization* [[LWB18]](#LWB18) in the version of Algorithm 4 of [[LWB18]](#LWB18) (`rSPF_HTP`).
+* `RiemAdaIHT`: *Adaptive Riemannian Iterative Hard Thresholding* as used in [[EKPU23]](#EKPU23), cf. also [repository here](https://github.com/maxpfeffer/riemannian_thresholding).
+
+## References
+ - **[KM23]** Christian Kümmerle and Johannes Maly, [**Recovering Simultaneously Structured Data via Non-Convex Iteratively Reweighted Least Squares**](https://openreview.net/pdf?id=50hs53Zb3w). _NeurIPS 2023_, 2023. <a name="KM23"></a>
+ - **[EKPU23]** Henrik Eisenmann, Felix Krahmer, Max Pfeffer, and André Uschmajew. [**Riemannian thresholding methods for row-sparse and low-rank matrix recovery**](https://doi.org/10.1007/s11075-022-01433-5). _Numerical Algorithms_, 93 (2):669–693, 2023. <a name="EKPU23"></a>
+ - **[LWB18]** Kiryung Lee, Yihong Wu, and Yoram Bresler. [**Near-optimal compressed sensing of a class of sparse low-rank matrices via sparse power factorization**](https://doi.org/10.1109/TIT.2017.2784479). IEEE Transactions on Information Theory, 64(3):1666–1698, 2018. <a name="LWB18"></a>

setup.m

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+% Run this script from the base folder of the repo 'simirls' before running
+% any code.
+addpath(genpath('algorithms'));
+addpath(genpath('data'));
+addpath(genpath('Examples'));
+addpath(genpath('experiment_setup'));
+addpath(genpath('experiments'));
+addpath(genpath('results'));
+addpath(genpath('utilities'))