Almost Phaseless Sampling for Spline Spaces with Arbitrary Knots*. (18th August 2021)

• Record Type: Journal Article
• Authors: Li, Rui; Zhang, Qingyue
• Is Part Of: Numerical functional analysis and optimization. Volume 42:Number 11(2021)
• Page Start: 1308
• Page End: 1322
• Publication Date: 2021-08-18
• Subjects: Almost phaseless sampling -- spline spaces -- arbitrary knots -- phase retrieval; 42C15 -- 42C40 -- 41A58; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.1957928
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: This article deals with almost phaseless sampling for spaces generated by B-splines with arbitrary knots. We provide a necessary and sufficient condition, which is a characterization of an almost phaseless sampling set, to admit phase recovery for almost all B-spline functions on an interval. Our results show that only N + 1 intensity measurements are sufficient to recover phase information for almost all functions in N dimensional B-spline function spaces with arbitrary knots.