Fast algorithms enabling optimization and deep learning for photoacoustic tomography in a circular detection geometry

Fuente: arXiv
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Hauptverfasser: Hauptmann, Andreas, Kunyansky, Leonid, Poimala, Jenni
Format: Preprint
Veröffentlicht: 2025
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author Hauptmann, Andreas
Kunyansky, Leonid
Poimala, Jenni
author_facet Hauptmann, Andreas
Kunyansky, Leonid
Poimala, Jenni
contents The inverse source problem arising in photoacoustic tomography and in several other coupled-physics modalities is frequently solved by iterative algorithms. Such algorithms are based on the minimization of a certain cost functional. In addition, novel deep learning techniques are currently being investigated to further improve such optimization approaches. All such methods require multiple applications of the operator defining the forward problem, and of its adjoint. In this paper, we present new asymptotically fast algorithms for numerical evaluation of the forward and adjoint operators, applicable in the circular acquisition geometry. For an $(n \times n)$ image, our algorithms compute these operators in $\mathcal{O}(n^2 \log n)$ floating point operations. We demonstrate the performance of our algorithms in numerical simulations, where they are used as an integral part of several iterative image reconstruction techniques: classic variational methods, such as non-negative least squares and total variation regularized least squares, as well as deep learning methods, such as learned primal dual. A Python implementation of our algorithms and computational examples is available to the general public.
format Preprint
id arxiv_https___arxiv_org_abs_2510_24687
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Fast algorithms enabling optimization and deep learning for photoacoustic tomography in a circular detection geometry
Hauptmann, Andreas
Kunyansky, Leonid
Poimala, Jenni
Image and Video Processing
Artificial Intelligence
Numerical Analysis
Analysis of PDEs
Optimization and Control
The inverse source problem arising in photoacoustic tomography and in several other coupled-physics modalities is frequently solved by iterative algorithms. Such algorithms are based on the minimization of a certain cost functional. In addition, novel deep learning techniques are currently being investigated to further improve such optimization approaches. All such methods require multiple applications of the operator defining the forward problem, and of its adjoint. In this paper, we present new asymptotically fast algorithms for numerical evaluation of the forward and adjoint operators, applicable in the circular acquisition geometry. For an $(n \times n)$ image, our algorithms compute these operators in $\mathcal{O}(n^2 \log n)$ floating point operations. We demonstrate the performance of our algorithms in numerical simulations, where they are used as an integral part of several iterative image reconstruction techniques: classic variational methods, such as non-negative least squares and total variation regularized least squares, as well as deep learning methods, such as learned primal dual. A Python implementation of our algorithms and computational examples is available to the general public.
title Fast algorithms enabling optimization and deep learning for photoacoustic tomography in a circular detection geometry
topic Image and Video Processing
Artificial Intelligence
Numerical Analysis
Analysis of PDEs
Optimization and Control
url https://arxiv.org/abs/2510.24687