Book contents
- Frontmatter
- Dedication
- Reviews
- Contents
- Figures
- Tables
- Preface
- Acknowledgments
- 1 Introduction
- 2 Positive Definite Kernels and Functions
- 3 RBF Interpolation and Polynomial Precision
- 4 Error Estimates and Examples of Kernels
- 5 On Uncertainty Principles and Shape Parameter Selection
- 6 Rational Kernels
- 7 Partition of Unity
- 8 Efficient Reduced-Basis Approximation
- 9 Approximating via Variably Scaled Discontinuous Kernels
- 10 Application of VSDKs to Magnetic Particle Imaging
- 11 Applications to Astronomical Imaging
- 12 Kernels in Machine Learning
- 13 Support Vector Machines and other Methods
- 14 Local-to-global SVMs
- 15 Learning Data-Driven Optimized Kernels
- 16 Choosing and Learning the Scaling Function for the VSKs
- 17 Kernels for Persistent Homology
- 18 Software
- 19 Conclusions
- References
- Index
11 - Applications to Astronomical Imaging
Published online by Cambridge University Press: 08 August 2026
Book contents
- Frontmatter
- Dedication
- Reviews
- Contents
- Figures
- Tables
- Preface
- Acknowledgments
- 1 Introduction
- 2 Positive Definite Kernels and Functions
- 3 RBF Interpolation and Polynomial Precision
- 4 Error Estimates and Examples of Kernels
- 5 On Uncertainty Principles and Shape Parameter Selection
- 6 Rational Kernels
- 7 Partition of Unity
- 8 Efficient Reduced-Basis Approximation
- 9 Approximating via Variably Scaled Discontinuous Kernels
- 10 Application of VSDKs to Magnetic Particle Imaging
- 11 Applications to Astronomical Imaging
- 12 Kernels in Machine Learning
- 13 Support Vector Machines and other Methods
- 14 Local-to-global SVMs
- 15 Learning Data-Driven Optimized Kernels
- 16 Choosing and Learning the Scaling Function for the VSKs
- 17 Kernels for Persistent Homology
- 18 Software
- 19 Conclusions
- References
- Index
Summary
Solar hard X-ray imaging from RHESSI observations presents a parametric Fourier imaging problem where visibility data are sampled at scattered spatial frequencies across multiple energy channels. We present a VSK-based interpolation/extrapolation framework that exploits spectral correlations between adjacent energy channels. Theoretical analysis establishes stability bounds and shows that using correlated reconstructions as scaling functions regularizes along the parameter direction. Applied to RHESSI flare data, this approach yields regularized photon spectra with reduced uncertainties compared to independent reconstructions.
Information
- Type
- Chapter
- Information
- Kernel-Based MethodsMilestones and New Trends, pp. 91 - 104Publisher: Cambridge University PressPrint publication year: 2026
Accessibility standard: Inaccessible, or known limited accessibility
Why this information is here
This section outlines the accessibility features of this content - including support for screen readers, full keyboard navigation and high-contrast display options. This may not be relevant for you.Accessibility Information
The PDF of this chapter is known to have missing or limited accessibility features.
We may be reviewing its accessibility for future improvement, but final compliance is
not yet assured and may be subject to legal exceptions. If you have any questions,
please contact
accessibility@cambridge.org.
Content Navigation
Table of contents navigation
Allows you to navigate directly to chapters, sections, or non‐text items through a linked table of contents, reducing the need for extensive scrolling.
Allows you to navigate directly to chapters, sections, or non‐text items through a linked table of contents, reducing the need for extensive scrolling.
Index navigation
Provides an interactive index, letting you go straight to where a term or subject appears in the text without manual searching.
Provides an interactive index, letting you go straight to where a term or subject appears in the text without manual searching.
Reading Order & Textual Equivalents
Single logical reading order
You will encounter all content (including footnotes, captions, etc.) in a clear, sequential flow, making it easier to follow with assistive tools like screen readers.
You will encounter all content (including footnotes, captions, etc.) in a clear, sequential flow, making it easier to follow with assistive tools like screen readers.
Short alternative textual descriptions
You get concise descriptions (for images, charts, or media clips), ensuring you do not miss crucial information when visual or audio elements are not accessible.
You get concise descriptions (for images, charts, or media clips), ensuring you do not miss crucial information when visual or audio elements are not accessible.