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r-local sensing: Improved algorithm and applications

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Citation Author(s):
Submitted by:
Ahmed Abbasi
Last updated:
13 May 2022 - 1:53pm
Document Type:
Presentation Slides
Document Year:
Presenters Name:
Ahmed Ali Abbasi



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×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.

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