Limited Angle Tomography

With Tatiana Bubba, University of Helsinki

Limited Angle Tomography: Inpanting in Phase Space by Deep Learning

Limited angle geometry is still a rather challenging modality in computed tomography (CT). Compared to the standard filtered back-projection (FBP), regularization-based methods, combined with iterative schemes, help in removing artifacts but still cannot deliver satisfactory reconstructions. Based on the result that limited tomographic datasets reveal parts of the wavefront (WF) set in a stable way and artifacts from limited angle CT have some directional property, we propose a method that combines, in the phase space, the information coming from the visible part of the WF set and ”inpaints” the invisible one by learning it with a convolutional neural network (CNN) architecture. The WF set information is accessed by using the directional features of shearlets combined with a compressed sensing formulation, which is well suited to derive visible and invisible coefficients. Compared to other recently proposed deep learning strategies for (limited data) CT, our method provides a superior performance, an (heuristic) understanding of why the method works, providing a more reliable approach especially for medical applications. This is a joint work with G. Kutyniok, M. Lassas, M. Marz, W. Samek, S. Siltanenand V. Srinivasan

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