# r-local sensing: Improved algorithm and applications

arXiv: https://arxiv.org/abs/2110.14034 · HTML: https://mlsanity.com/paper/2110.14034/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Oct 2021.

## Built on by (most cited first, 4 of 4)

- [Shuffled Multi-Channel Sparse Signal Recovery](https://mlsanity.com/paper/2212.07368/) (2022)
- [Alternating minimization algorithm with initialization analysis for r-local and k-sparse unlabeled sensing](https://mlsanity.com/paper/2211.07621/) (2022)
- [AltGDmin: Alternating GD and Minimization for Partly-Decoupled (Federated) Optimization](https://mlsanity.com/paper/2504.14741/) (2025)
- [Cross-Channel Unlabeled Sensing over a Union of Signal Subspaces](https://mlsanity.com/paper/2506.09773/) (2025)

## Abstract (arXiv)

The unlabeled sensing problem is to solve a noisy linear system of equations under unknown permutation of the measurements. We study a particular case of the problem where the permutations are restricted to be r-local, i.e. the permutation matrix is block diagonal with r x r blocks. Assuming a Gaussian measurement matrix, we argue that the r-local permutation model is more challenging compared to a recent sparse permutation model. We propose a proximal alternating minimization algorithm for the general unlabeled sensing problem that provably converges to a first order stationary point. Applied to the r-local model, we show that the resulting algorithm is efficient. We validate the algorithm on synthetic and real datasets. We also formulate the 1-d unassigned distance geometry problem as an unlabeled sensing problem with a structured measurement matrix.