Butterfly Transforms for Efficient Representation of Spatially Variant Point Spread Functions in Bayesian Imaging
Author:
Eberle Vincent12ORCID, Frank Philipp1ORCID, Stadler Julia1, Streit Silvan3ORCID, Enßlin Torsten12ORCID
Affiliation:
1. Max Planck Institute for Astrophysics, Karl-Schwarzschild-Straße 1, 85748 Garching, Germany 2. Faculty of Physics, Ludwig-Maximilians-Universität München (LMU), Geschwister-Scholl-Platz 1, 80539 München, Germany 3. Fraunhofer Institute for Applied and Integrated Security AISEC, Lichtenbergstraße 11, 85748 Garching, Germany
Abstract
Bayesian imaging algorithms are becoming increasingly important in, e.g., astronomy, medicine and biology. Given that many of these algorithms compute iterative solutions to high-dimensional inverse problems, the efficiency and accuracy of the instrument response representation are of high importance for the imaging process. For efficiency reasons, point spread functions, which make up a large fraction of the response functions of telescopes and microscopes, are usually assumed to be spatially invariant in a given field of view and can thus be represented by a convolution. For many instruments, this assumption does not hold and degrades the accuracy of the instrument representation. Here, we discuss the application of butterfly transforms, which are linear neural network structures whose sizes scale sub-quadratically with the number of data points. Butterfly transforms are efficient by design, since they are inspired by the structure of the Cooley–Tukey fast Fourier transform. In this work, we combine them in several ways into butterfly networks, compare the different architectures with respect to their performance and identify a representation that is suitable for the efficient representation of a synthetic spatially variant point spread function up to a 1% error. Furthermore, we show its application in a short synthetic example.
Funder
German Aerospace Center Deutsche Forschungsgemeinschaft
Subject
General Physics and Astronomy
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