r-local sensing: Improved algorithm and applications

Code

• github.com/aabbas02/r-local-unlabeled-sensing
  OfficialIn papernone★ 0
• github.com/aabbas02/proximal-alt-min-for-uls-udgp
  OfficialIn papernone★ 0

Abstract

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.

Reproductions