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

Area of Science:

• Computational imaging
• Applied mathematics
• Machine learning

Background:

• Bayesian imaging algorithms are crucial in fields like astronomy, medicine, and biology.
• Efficient and accurate instrument response representation is vital for high-dimensional inverse problems in imaging.
• The assumption of spatially invariant point spread functions (PSFs) often limits accuracy in real-world instruments.

Purpose of the Study:

• To explore the application of butterfly transforms for representing spatially variant point spread functions (PSFs).
• To develop and compare different butterfly network architectures for efficient and accurate PSF representation.
• To demonstrate the utility of butterfly networks in Bayesian imaging.

Main Methods:

• Utilized butterfly transforms, a type of neural network with sub-quadratic scaling, inspired by the Cooley-Tukey fast Fourier transform.
• Constructed and evaluated various butterfly network architectures.
• Tested the representation of a synthetic spatially variant PSF.

Main Results:

• Identified a butterfly network architecture capable of representing a synthetic spatially variant PSF with up to 1% error.
• Demonstrated the efficiency of butterfly networks in handling complex instrument response functions.
• Showcased a synthetic example application of the developed method.

Conclusions:

• Butterfly networks offer an efficient and accurate solution for representing spatially variant PSFs in Bayesian imaging.
• This approach overcomes limitations of traditional spatially invariant assumptions.
• The findings have significant implications for improving imaging quality in various scientific domains.