A Field-Theoretic View of Unlabeled Sensing

Autor:	Liang, Hao, Lu, Jingyu, Tsakiris, Manolis C., Zhi, Lihong
Rok vydání:	2023
Předmět:	Mathematics - Commutative Algebra Computer Science - Information Theory Electrical Engineering and Systems Science - Signal Processing
Druh dokumentu:	Working Paper
Popis:	Unlabeled sensing is the problem of solving a linear system of equations, where the right-hand-side vector is known only up to a permutation. In this work, we study fields of rational functions related to symmetric polynomials and their images under a linear projection of the variables; as a consequence, we establish that the solution to an n-dimensional unlabeled sensing problem with generic data can be obtained as the unique solution to a system of n + 1 polynomial equations of degrees 1, 2, . . . , n + 1 in n unknowns. Besides the new theoretical insights, this development offers the potential for scaling up algebraic unlabeled sensing algorithms. Comment: 12 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2303.01175 Zobrazit plný text záznamu View this record from Arxiv