Deep Learning of truncated singular values for limited view photoacoustic tomography

Johannes Schwab; Stephan Antholzer; Robert Nuster; Günther Paltauf; Markus Haltmeier

doi:10.1117/12.2508418

27 February 2019 Deep Learning of truncated singular values for limited view photoacoustic tomography

Johannes Schwab, Stephan Antholzer, Robert Nuster, Günther Paltauf, Markus Haltmeier

Proceedings Volume 10878, Photons Plus Ultrasound: Imaging and Sensing 2019; 1087836 (2019) https://doi.org/10.1117/12.2508418
Event: SPIE BiOS, 2019, San Francisco, California, United States

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.

Citation Download Citation

Johannes Schwab, Stephan Antholzer, Robert Nuster, Günther Paltauf, and Markus Haltmeier "Deep Learning of truncated singular values for limited view photoacoustic tomography", Proc. SPIE 10878, Photons Plus Ultrasound: Imaging and Sensing 2019, 1087836 (27 February 2019); https://doi.org/10.1117/12.2508418

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