# Orthogonally weighted ℓ2,1 regularization for rank-aware joint sparse recovery: algorithm and analysis

arXiv: https://arxiv.org/abs/2311.12282 · HTML: https://mlsanity.com/paper/2311.12282/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 53 references that are in the map.
- First posted on arXiv 21 Nov 2023.

## Builds on (most cited first, 5 of 5)

- [Robust CUR Decomposition: Theory and Imaging Applications](https://mlsanity.com/paper/2101.05231/) (2021)
- [A Scale Invariant Approach for Sparse Signal Recovery](https://mlsanity.com/paper/1812.08852/) (2018)
- [A Method for Finding Structured Sparse Solutions to Non-negative Least Squares Problems with Applications](https://mlsanity.com/paper/1301.0413/) (2013)
- [Analysis and algorithms for some compressed sensing models based on L1/L2 minimization](https://mlsanity.com/paper/2007.12821/) (2020)
- [On the strong convergence of forward-backward splitting in reconstructing jointly sparse signals](https://mlsanity.com/paper/1711.02591/) (2017)

## Abstract (arXiv)

We propose and analyze an efficient algorithm for solving the joint sparse recovery problem using a new regularization-based method, named orthogonally weighted ℓ2,1 (mathitowℓ2,1), which is specifically designed to take into account the rank of the solution matrix. This method has applications in feature extraction, matrix column selection, and dictionary learning, and it is distinct from commonly used ℓ2,1 regularization and other existing regularization-based approaches because it can exploit the full rank of the row-sparse solution matrix, a key feature in many applications. We provide a proof of the method's rank-awareness, establish the existence of solutions to the proposed optimization problem, and develop an efficient algorithm for solving it, whose convergence is analyzed. We also present numerical experiments to illustrate the theory and demonstrate the effectiveness of our method on real-life problems.