Efficient Representations of Spatially Variant Point Spread Functions with Butterfly Transforms in Bayesian Imaging Algorithms

Eberle, Vincent; Frank, Philipp; Stadler, Julia; Streit, Silvan; Enßlin, T. A.

doi:10.3390/psf2022005033

Cited by 3 publications

(3 citation statements)

References 9 publications

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“…Our contribution to the field demonstrates the application of butterfly transforms to efficiently represent spatially varying point spread functions, necessary for accurate Bayesian imaging. A proceeding paper presented an early stage of this work [ 19 ]. In this article, however, we go more into the details of the method, theoretically address the scaling of the networks, and introduce error maps as a new visualisation method.…”

Section: Related Workmentioning

confidence: 99%

Butterfly Transforms for Efficient Representation of Spatially Variant Point Spread Functions in Bayesian Imaging

Eberle

Frank

Stadler

et al. 2023

Entropy

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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.

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Section: Related Workmentioning

confidence: 99%

Butterfly Transforms for Efficient Representation of Spatially Variant Point Spread Functions in Bayesian Imaging

Eberle

Frank

Stadler

et al. 2023

Entropy

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“…Gaussian process regression, also known as "Kriging", has been extensively studied for several decades [11]. GPs have become one of the most popular classes of machine learning [12] and Bayesian models [13], and found wide application in the field of "Uncertainty Quantification" [14,15]. The defining element of a Gaussian process is its covariance function, also referred to as the kernel.…”

Section: Physics-consistent Gaussian Processesmentioning

confidence: 99%

Physics-Consistency Condition for Infinite Neural Networks and Experimental Characterization

Ranftl,

Guan

2023

The 42nd International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering

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“…We expect NIFTy.re to be highly useful for many imaging applications and envision many applications within and outside of astrophysics Arras et al, 2022;Eberle et al, 2022Eberle et al, , 2023Frank et al, 2017;S. Hutschenreuter et al, 2022;Sebastian Hutschenreuter et al, 2023;Leike et al, 2020;Mertsch & Phan, 2023;J.…”

mentioning

confidence: 99%

Re-Envisioning Numerical Information Field Theory (NIFTy.re): A Library for Gaussian Processes and Variational Inference

Edenhofer,

Frank,

Roth

et al. 2024

JOSS

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Efficient Representations of Spatially Variant Point Spread Functions with Butterfly Transforms in Bayesian Imaging Algorithms

Cited by 3 publications

References 9 publications

Butterfly Transforms for Efficient Representation of Spatially Variant Point Spread Functions in Bayesian Imaging

Butterfly Transforms for Efficient Representation of Spatially Variant Point Spread Functions in Bayesian Imaging

Physics-Consistency Condition for Infinite Neural Networks and Experimental Characterization

Re-Envisioning Numerical Information Field Theory (NIFTy.re): A Library for Gaussian Processes and Variational Inference

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