# Deep Learning of truncated singular values for limited view photoacoustic tomography

## TL;DR

This paper introduces a novel two-step deep learning approach for photoacoustic image reconstruction from limited view data, combining truncated SVD with neural networks to improve image quality in ill-posed inverse problems.

## Contribution

It proposes a data-driven regularization method that enhances truncated SVD reconstructions using deep neural networks, applicable to various inverse problems.

## Key findings

- Significant improvement over pure truncated SVD reconstructions.
- Effective noise suppression in limited view photoacoustic imaging.
- Framework adaptable to other inverse problems with known SVD.

## Abstract

We develop a data-driven regularization method for the severely ill-posed problem of photoacoustic image reconstruction from limited view data. Our approach is based on the regularizing networks that have been recently introduced and analyzed in [J. Schwab, S. Antholzer, and M. Haltmeier. Big in Japan: Regularizing networks for solving inverse problems (2018), arXiv:1812.00965] and consists of two steps. In the first step, an intermediate reconstruction is performed by applying truncated singular value decomposition (SVD). In order to prevent noise amplification, only coefficients corresponding to sufficiently large singular values are used, whereas the remaining coefficients are set zero. In a second step, a trained deep neural network is applied to recover the truncated SVD coefficients. Numerical results are presented demonstrating that the proposed data driven estimation of the truncated singular values significantly improves the pure truncated SVD reconstruction. We point out that proposed reconstruction framework can straightforwardly be applied to other inverse problems, where the SVD is either known analytically or can be computed numerically.