# On Learning the Invisible in Photoacoustic Tomography with Flat Directionally Sensitive Detector

arXiv: https://arxiv.org/abs/2204.10001 · HTML: https://mlsanity.com/paper/2204.10001/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 70 references that are in the map.
- First posted on arXiv 21 Apr 2022.

## Builds on (most cited first, 20 of 20)

- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [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)
- [Image reconstruction by domain transform manifold learning](https://mlsanity.com/paper/1704.08841/) (2017)
- [Solving ill-posed inverse problems using iterative deep neural networks](https://mlsanity.com/paper/1704.04058/) (2017)
- [A deep convolutional neural network using directional wavelets for low-dose X-ray CT reconstruction](https://mlsanity.com/paper/1610.09736/) (2016)
- [Fully Dense UNet for 2D Sparse Photoacoustic Tomography Artifact Removal](https://mlsanity.com/paper/1808.10848/) (2018)
- [Model based learning for accelerated, limited-view 3D photoacoustic tomography](https://mlsanity.com/paper/1708.09832/) (2017)
- [Learning The Invisible: A Hybrid Deep Learning-Shearlet Framework for Limited Angle Computed Tomography](https://mlsanity.com/paper/1811.04602/) (2018)
- [Deep Learning in Photoacoustic Tomography: Current approaches and future directions](https://mlsanity.com/paper/2009.07608/) (2020)
- [Deep Learning for Photoacoustic Tomography from Sparse Data](https://mlsanity.com/paper/1704.04587/) (2017)
- [Deep neural networks for inverse problems with pseudodifferential operators: an application to limited-angle tomography](https://mlsanity.com/paper/2006.01620/) (2020)
- [A Partially Learned Algorithm for Joint Photoacoustic Reconstruction and Segmentation](https://mlsanity.com/paper/1906.07499/) (2019)
- [Approximate k-space models and Deep Learning for fast photoacoustic reconstruction](https://mlsanity.com/paper/1807.03191/) (2018)
- [Simultaneous reconstruction of the initial pressure and sound speed in photoacoustic tomography using a deep-learning approach](https://mlsanity.com/paper/1907.09951/) (2019)
- [Extraction of digital wavefront sets using applied harmonic analysis and deep neural networks](https://mlsanity.com/paper/1901.01388/) (2019)
- [Deep Microlocal Reconstruction for Limited-Angle Tomography](https://mlsanity.com/paper/2108.05732/) (2021)
- [Y-Net: A Hybrid Deep Learning Reconstruction Framework for Photoacoustic Imaging in vivo](https://mlsanity.com/paper/1908.00975/) (2019)
- [Photoacoustic Reconstruction Using Sparsity in Curvelet Frame: Image versus Data Domain](https://mlsanity.com/paper/2011.13080/) (2020)
- [Learned backprojection for sparse and limited view photoacoustic tomography](https://mlsanity.com/paper/1908.00593/) (2019)

## Built on by (most cited first, 2 of 2)

- [Learned Interferometric Imaging for the SPIDER Instrument](https://mlsanity.com/paper/2301.10260/) (2023)
- [Automated Construction of Artificial Lattice Structures with Designer Electronic States](https://mlsanity.com/paper/2508.02581/) (2025)

## Abstract (arXiv)

In photoacoustic tomography (PAT) with flat sensor, we routinely encounter two types of limited data. The first is due to using a finite sensor and is especially perceptible if the region of interest is large relative to the sensor or located farther away from the sensor. In this paper, we focus on the second type caused by a varying sensitivity of the sensor to the incoming wavefront direction which can be modelled as binary i.e. by a cone of sensitivity. Such visibility conditions result, in the Fourier domain, in a restriction of both the image and the data to a bow-tie, akin to the one corresponding to the range of the forward operator. The visible wavefrontsets in image and data domains, are related by the wavefront direction mapping. We adapt the wedge restricted Curvelet decomposition, we previously proposed for the representation of the full PAT data, to separate the visible and invisible wavefronts in the image. We optimally combine fast approximate operators with tailored deep neural network architectures into efficient learned reconstruction methods which perform reconstruction of the visible coefficients and the invisible coefficients are learned from a training set of similar data.