# Deep learning versus $\ell^1$-minimization for compressed sensing photoacoustic tomography

## TL;DR

This paper compares deep learning methods and $ ext{l}^1$-minimization for compressed sensing in photoacoustic tomography, showing deep learning excels with deterministic measurements while $ ext{l}^1$-minimization is better with Bernoulli measurements.

## Contribution

It provides a comparative analysis of deep learning and $ ext{l}^1$-minimization techniques for CS in PAT, highlighting their relative performance under different measurement schemes.

## Key findings

- Deep learning yields more accurate results with deterministic measurements.
- $ ext{l}^1$-minimization outperforms deep learning with Bernoulli measurements.
- Nullspace network outperforms residual network in MSE.

## Abstract

We investigate compressed sensing (CS) techniques for reducing the number of measurements in photoacoustic tomography (PAT). High resolution imaging from CS data requires particular image reconstruction algorithms. The most established reconstruction techniques for that purpose use sparsity and $\ell^1$-minimization. Recently, deep learning appeared as a new paradigm for CS and other inverse problems. In this paper, we compare a recently invented joint $\ell^1$-minimization algorithm with two deep learning methods, namely a residual network and an approximate nullspace network. We present numerical results showing that all developed techniques perform well for deterministic sparse measurements as well as for random Bernoulli measurements. For the deterministic sampling, deep learning shows more accurate results, whereas for Bernoulli measurements the $\ell^1$-minimization algorithm performs best. Comparing the implemented deep learning approaches, we show that the nullspace network uniformly outperforms the residual network in terms of the mean squared error (MSE).