Research Paper#Signal Processing, Phase Retrieval, Reproducing Kernel Hilbert Spaces🔬 ResearchAnalyzed: Jan 3, 2026 15:53
Cheeger Bounds for Stable Phase Retrieval in RKHS
Published:Dec 30, 2025 12:01
•1 min read
•ArXiv
Analysis
This paper investigates the stability of phase retrieval, a crucial problem in signal processing, particularly when dealing with noisy measurements. It introduces a novel framework using reproducing kernel Hilbert spaces (RKHS) and a kernel Cheeger constant to quantify connectedness and derive stability certificates. The work provides unified bounds for both real and complex fields, covering various measurement domains and offering insights into generalized wavelet phase retrieval. The use of Cheeger-type estimates provides a valuable tool for analyzing the stability of phase retrieval algorithms.
Key Takeaways
- •Introduces a kernel Cheeger constant for analyzing phase retrieval stability.
- •Provides unified stability bounds for real and complex fields.
- •Covers finite- and infinite-dimensional settings and various measurement domains.
- •Applies the framework to generalized wavelet phase retrieval.
Reference
“The paper introduces a kernel Cheeger constant that quantifies connectedness relative to kernel localization, yielding a clean stability certificate.”