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.
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