# Item

ITEM ACTIONSEXPORT

Released

Journal Article

#### Butterfly transforms for efficient representation of spatially variant point spread functions in Bayesian imaging

##### MPS-Authors

##### External Resource

No external resources are shared

##### Fulltext (restricted access)

There are currently no full texts shared for your IP range.

##### Fulltext (public)

There are no public fulltexts stored in PuRe

##### Supplementary Material (public)

There is no public supplementary material available

##### Citation

Eberle, V., Frank, P., Stadler, J., Streit, S., & Enßlin, T. (2023). Butterfly
transforms for efficient representation of spatially variant point spread functions in Bayesian imaging.*
Entropy,* *25*(4): 652. doi:10.3390/e25040652.

Cite as: https://hdl.handle.net/21.11116/0000-000D-A762-8

##### 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.