# Efficient Structured Matrix Rank Minimization

arXiv: https://arxiv.org/abs/1509.02447 · HTML: https://mlsanity.com/paper/1509.02447/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Sep 2015.

## Built on by (most cited first, 1 of 1)

- [Model-based Reconstruction with Learning: From Unsupervised to Supervised and Beyond](https://mlsanity.com/paper/2103.14528/) (2021)

## Abstract (arXiv)

We study the problem of finding structured low-rank matrices using nuclear norm regularization where the structure is encoded by a linear map. In contrast to most known approaches for linearly structured rank minimization, we do not (a) use the full SVD, nor (b) resort to augmented Lagrangian techniques, nor (c) solve linear systems per iteration. Instead, we formulate the problem differently so that it is amenable to a generalized conditional gradient method, which results in a practical improvement with low per iteration computational cost. Numerical results show that our approach significantly outperforms state-of-the-art competitors in terms of running time, while effectively recovering low rank solutions in stochastic system realization and spectral compressed sensing problems.