Noisy Low Rank Column-wise Sensing

This letter studies the AltGDmin algorithm for solving the noisy low rank column-wise sensing (LRCS) problem. Our sample complexity guarantee improves upon the best existing one by a factor $\max(r, \log(1/\epsilon))/r$ where $r$ is the rank of the unknown matrix and $\epsilon$ is the final desired accuracy. A second contribution of this work is a detailed comparison of guarantees from all work that studies the exact same mathematical problem as LRCS, but refers to it by different names.

@article{singh2025_2409.08384,
  title={ Noisy Low Rank Column-wise Sensing },
  author={ Ankit Pratap Singh and Namrata Vaswani },
  journal={arXiv preprint arXiv:2409.08384},
  year={ 2025 }
}