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

arXiv: https://arxiv.org/abs/2510.24687 · HTML: https://mlsanity.com/paper/2510.24687/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 52 references that are in the map.
- First posted on arXiv 28 Oct 2025.

## Builds on (most cited first, 10 of 10)

- [Learning a Variational Network for Reconstruction of Accelerated MRI Data](https://mlsanity.com/paper/1704.00447/) (2017)
- [Learned Primal-dual Reconstruction](https://mlsanity.com/paper/1707.06474/) (2017)
- [Solving ill-posed inverse problems using iterative deep neural networks](https://mlsanity.com/paper/1704.04058/) (2017)
- [Model based learning for accelerated, limited-view 3D photoacoustic tomography](https://mlsanity.com/paper/1708.09832/) (2017)
- [Deep Learning in Photoacoustic Tomography: Current approaches and future directions](https://mlsanity.com/paper/2009.07608/) (2020)
- [Deep learning for biomedical photoacoustic imaging: A review](https://mlsanity.com/paper/2011.02744/) (2020)
- [Approximate k-space models and Deep Learning for fast photoacoustic reconstruction](https://mlsanity.com/paper/1807.03191/) (2018)
- [Model-corrected learned primal-dual models for fast limited-view photoacoustic tomography](https://mlsanity.com/paper/2304.01963/) (2023)
- [Digital twins enable full-reference quality assessment of photoacoustic image reconstructions](https://mlsanity.com/paper/2505.24514/) (2025)
- [A Direct Method for Photoacoustic Tomography with Inhomogeneous Sound Speed](https://mlsanity.com/paper/1507.01741/) (2015)

## Built on by (most cited first, 1 of 1)

- [Deep Image Prior for photoacoustic tomography can mitigate limited-view artifacts](https://mlsanity.com/paper/2604.19176/) (2026)

## Abstract (arXiv)

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 × n) image, our algorithms compute these operators in O(n2 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.