Simultaneous PSF Matching via Dual Kernel Optimization

RAS Techniques and Instruments

Abstract

Abstract Standard point spread function (PSF) matching algorithms consider one image as the reference and aim to find a convolution kernel such that, when applied to the reference image, the PSFs of the reference and non-reference images are matched. This method works well if one image is a degraded version of the other. However, this is not always the case: if the PSFs of the two images have different orientations or shapes, a simple convolution of one of the images does not lead to a satisfactory match. While this can be trivially solved by convolving the first PSF with the second and vice-versa, this results in unnecessarily large PSFs. In this paper, we present a new algorithm, Dual Kernel Optimization (DKO), that simultaneously solves for two convolution kernels, one for each image, such that the PSFs match and the sizes of the kernels are minimized. This results in a minimally-degraded final set of PSFs. Since this problem is highly degenerate, we use Stochastic Gradient Langevin Dynamics (SGLD) which rigorously explores the parameter space and converges on the globally-optimal solution. We discuss the algorithmic challenges for this problem and the modifications to standard SGLD used to constrain it. Finally, we include a discussion on the application of this methodology to real-world images, including cases where the PSF varies over the field of view.

Authors 9

1. Carter Lee Rhea

   Centre for Research in Astrophysics of Québec

   Affiliation as printed

   Centre de recherche en astrophysique du Québec (CRAQ) , Québec, QC G1V 0A6 ,

   Dragonfly Focused Research Organization , 150 Washington Avenue, Santa Fe, NM 87501 ,

2. Pieter Van Dokkum

   Yale University

   Affiliation as printed

   Dragonfly Focused Research Organization , 150 Washington Avenue, Santa Fe, NM 87501 ,

   Yale University Astronomy Department, , 219 Prospect St, New Haven, CT 06511 ,

3. Roberto Abraham

   Canadian Institute for Theoretical Astrophysics

   Affiliation as printed

   Dragonfly Focused Research Organization , 150 Washington Avenue, Santa Fe, NM 87501 ,

   Dunlap Institute for Astronomy & Astrophysics, University of Toronto , 50 St. George Street, Toronto, ON M5S3H4 ,

   University of Toronto David A. Dunlap Department of Astronomy, and Astrophysics, , 50 St. George Street, Toronto, ON M5S3H4 ,

4. Imad Pasha

   Yale University

   Affiliation as printed

   Dragonfly Focused Research Organization , 150 Washington Avenue, Santa Fe, NM 87501 ,

   Yale University Astronomy Department, , 219 Prospect St, New Haven, CT 06511 ,

5. Steven R. Janssens
   Affiliation as printed

   Dragonfly Focused Research Organization , 150 Washington Avenue, Santa Fe, NM 87501 ,

6. William P. Bowman

   Yale University

   Affiliation as printed

   Dragonfly Focused Research Organization , 150 Washington Avenue, Santa Fe, NM 87501 ,

   Yale University Astronomy Department, , 219 Prospect St, New Haven, CT 06511 ,

7. Deborah Lokhorst

   Herzberg Institute of Astrophysics

   Affiliation as printed

   Dragonfly Focused Research Organization , 150 Washington Avenue, Santa Fe, NM 87501 ,

   NRC Herzberg Astronomy & Astrophysics Research Centre , 5071 West Saanich Road, Victoria, BC V9E 2E7 ,

8. Seery Chen

   Canadian Institute for Theoretical Astrophysics

   Affiliation as printed

   Dragonfly Focused Research Organization , 150 Washington Avenue, Santa Fe, NM 87501 ,

   Dunlap Institute for Astronomy & Astrophysics, University of Toronto , 50 St. George Street, Toronto, ON M5S3H4 ,

   University of Toronto David A. Dunlap Department of Astronomy, and Astrophysics, , 50 St. George Street, Toronto, ON M5S3H4 ,

9. Qing Lui Aachen Leiden Observatory

   Leiden University · Leiden Observatory

   Affiliation as printed

   Leiden Observatory, Leiden University , P.O. Box 9513, 2300 RA Leiden ,