Deep Learning for Photoacoustic Tomography from Sparse Data (1704.04587v3)

Abstract: The development of fast and accurate image reconstruction algorithms is a central aspect of computed tomography. In this paper, we investigate this issue for the sparse data problem in photoacoustic tomography (PAT). We develop a direct and highly efficient reconstruction algorithm based on deep learning. In our approach image reconstruction is performed with a deep convolutional neural network (CNN), whose weights are adjusted prior to the actual image reconstruction based on a set of training data. The proposed reconstruction approach can be interpreted as a network that uses the PAT filtered backprojection algorithm for the first layer, followed by the U-net architecture for the remaining layers. Actual image reconstruction with deep learning consists in one evaluation of the trained CNN, which does not require time consuming solution of the forward and adjoint problems. At the same time, our numerical results demonstrate that the proposed deep learning approach reconstructs images with a quality comparable to state of the art iterative approaches for PAT from sparse data.

• The paper presents a deep learning framework that integrates linear FBP reconstruction with a U-net CNN to remove artifacts in PAT images.
• It demonstrates that the CNN approach achieves image quality comparable to iterative methods while significantly reducing computational costs.
• The results suggest promising future research directions for extending the method to complex 3D data and various measurement geometries.

Deep Learning for Photoacoustic Tomography from Sparse Data

The paper "Deep Learning for Photoacoustic Tomography from Sparse Data" by Antholzer, Haltmeier, and Schwab presents a novel approach to enhancing photoacoustic tomography (PAT) image reconstruction by leveraging the capabilities of deep learning. Specifically, the authors introduce a methodology utilizing a convolutional neural network (CNN) to address the challenges posed by sparse data in PAT.

Overview of the Methodology

The primary focus of this paper is the development of an efficient and direct image reconstruction algorithm that leverages deep learning techniques. The approach is a two-step hybrid methodology:

1. Linear Reconstruction Preprocessing: An initial linear reconstruction algorithm, such as filtered backprojection (FBP), is applied to the sparse data. This step yields a preliminary reconstructed image that typically contains undersampling artifacts due to the sparsity of the data.
2. Artifact Removal via CNN: A deep CNN, specifically utilizing the U-net architecture, is then deployed to process this preliminary image, effectively removing artifacts and enhancing the overall image quality. The U-net is originally designed for biomedical image segmentation but is adapted here for image reconstruction.

The design of the CNN incorporates the traditional PAT FBP algorithm as its initial layer, followed by the U-net to enhance image quality. This integration allows for efficient reconstruction without iterative processing, thereby significantly reducing computational costs compared to traditional iterative approaches.

Numerical Results and Claims

The paper's numerical experiments demonstrate that the proposed deep learning-based method provides image quality that is comparable to—or even surpassing—state-of-the-art iterative reconstruction techniques. The method achieves this without requiring iterative evaluations of forward and adjoint models, thus ensuring computational efficiency. In comparisons including both exact and noise-corrupted datasets, images reconstructed via the deep learning approach show reduced artifacts compared to those processed through traditional FBP alone or through TV-regularization-based iterative approaches.

Implications and Future Developments

Practically, the proposed method holds significant promise for clinical and research applications of PAT, where rapid and reliable imaging is critical. The use of deep learning circumvents the need for explicit a priori models about the structures being imaged; instead, it learns from training data explicitly characterizing the desired features and quality of reconstructed images.

Theoretically, this work paves the way for further exploration of deep neural networks in solving inverse problems, employing a purely data-driven manner to automatically adjust for optimal reconstruction outputs. Future research directions suggested include extending the network to handle more complex three-dimensional data and integrating the methodology with different measurement geometries. Additionally, expanding the training datasets to include more realistic phantoms could potentially enhance the robustness and applicability of the model, ensuring its efficacy across a broader range of imaging scenarios.

This paper contributes a significant advancement in PAT, demonstrating the utility of deep learning in improving image reconstruction quality while maintaining computational efficiency, especially in cases of data sparsity. This work is indicative of the broader trends in applying deep learning to complex inverse problems across diverse scientific and engineering domains.