2021/03/12 by Yanting Ma, Petros T. Boufounos, Ma, Yanting +5
Engineering · Mathematics · Medicine · #68U10 (Secondary) #94A08 (Primary) #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Electrical engineering #I.4.8 #Image and Video Processing (eess.IV) #Information Theory (cs.IT) #Machine Learning (cs.LG) #Mathematical Analysis and Transform Methods #Medical Imaging Techniques and Applications #Signal Processing (eess.SP) #Sparse and Compressive Sensing Techniques #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2103.07458
openalex publication_date 2021/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In several applications, including imaging of deformable objects while in motion, simultaneous localization and mapping, and unlabeled sensing, we encounter the problem of recovering a signal that is measured subject to unknown permutations. In this paper we take a fresh look at this problem through the lens of optimal transport (OT). In particular, we recognize that in most practical applications the unknown permutations are not arbitrary but some are more likely to occur than others. We exploit this by introducing a regularization function that promotes the more likely permutations in the solution. We show that, even though the general problem is not convex, an appropriate relaxation of the resulting regularized problem allows us to exploit the well-developed machinery of OT and develop a tractable algorithm.