Additive stability of frames: Additive stability of frames

Given a frame in a finite dimensional Hilbert space we construct additive perturbations which decrease the condition number of the frame. By iterating this perturbation, we introduce an algorithm that produces a tight frame in a finite number of steps. Additionally, we give sharp bounds on additive...

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Bibliographic Details
Published in:Sampling theory, signal processing, and data analysis signal processing, and data analysis, 2024-12, Vol.22 (2), Article 20
Main Authors: Asipchuk, Oleg, Glidewell, Jacob, Rodriguez, Luis
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Machine Learning
Mathematics
Mathematics and Statistics
Original Article
Signal,Image and Speech Processing
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Summary:Given a frame in a finite dimensional Hilbert space we construct additive perturbations which decrease the condition number of the frame. By iterating this perturbation, we introduce an algorithm that produces a tight frame in a finite number of steps. Additionally, we give sharp bounds on additive perturbations which preserve frames and we study the effect of appending and erasing vectors to a given tight frame. We also discuss under which conditions our finite-dimensional results are extendable to infinite-dimensional Hilbert spaces.
ISSN:2730-5716
2730-5724
DOI:10.1007/s43670-024-00094-w