We discuss several methods for image reconstruction in compressed sensing photoacoustic tomography (CS-PAT). In particular, we apply the deep learning method of [H. Li, J. Schwab, S. Antholzer, and M. Haltmeier. NETT: Solving Inverse Problems with Deep Neural Networks (2018), arXiv:1803.00092], which is based on a learned regularizer, for the first time to the CS-PAT problem. We propose a network architecture and training strategy for the NETT that we expect to be useful for other inverse problems as well. All algorithms are compared and evaluated on simulated data, and validated using experimental data for two different types of phantoms. The results one the hand indicate great potential of deep learning methods, and on the other hand show that significant future work is required to improve their performance on real-word data.
Filtered backprojection (FBP) is an efficient and popular class of tomographic image reconstruction methods. In photoacoustic tomography, these algorithms are based on theoretically exact analytic inversion formulas which results in accurate reconstructions. However, photoacoustic measurement data are often incomplete (limited detection view and sparse sampling), which results in artefacts in the images reconstructed with FBP. In addition to that, properties such as directivity of the acoustic detectors are not accounted for in standard FBP, which affects the reconstruction quality, too. To account for these issues, in this papers we propose to improve FBP algorithms based on machine learning techniques. In the proposed method, we include additional weight factors in the FBP, that are optimized on a set of incomplete data and the corresponding ground truth photoacoustic source. Numerical tests show that the learned FBP improves the reconstruction quality compared to the standard FBP.
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.
Applying standard algorithms to sparse data problems in photoacoustic tomography (PAT) yields low-quality images containing severe under-sampling artifacts. To some extent, these artifacts can be reduced by iterative image reconstruction algorithms which allow to include prior knowledge such as smoothness, total variation (TV) or sparsity constraints. These algorithms tend to be time consuming as the forward and adjoint problems have to be solved repeatedly. Further, iterative algorithms have additional drawbacks. For example, the reconstruction quality strongly depends on a-priori model assumptions about the objects to be recovered, which are often not strictly satisfied in practical applications. To overcome these issues, in this paper, we develop direct and efficient reconstruction algorithms based on deep learning. As opposed to iterative algorithms, we apply a convolutional neural network, whose parameters are trained before the reconstruction process based on a set of training data. For actual image reconstruction, a single evaluation of the trained network yields the desired result. Our presented numerical results (using two different network architectures) demonstrate that the proposed deep learning approach reconstructs images with a quality comparable to state of the art iterative reconstruction methods.
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