Operator Learning Approach for the Limited View Problem in Photoacoustic Tomography

Abstract

In photoacoustic tomography, one is interested to recover the initial pressure distribution inside a tissue from the corresponding measurements of the induced acoustic wave on the boundary of a region enclosing the tissue. In the limited view problem, the wave boundary measurements are given on the part of the boundary, whereas in the full view problem, the measurements are known on the whole boundary. For the full view problem, there exist various fast and robust reconstruction methods. These methods give severe reconstruction artifacts when they are applied directly to the limited view data. One approach for reducing such artefacts is trying to extend the limited view data to the whole region boundary, and then use existing reconstruction methods for the full view data. In this paper, we propose an operator learning approach for constructing an operator that gives an approximate extension of the limited view data. We consider the behavior of a reconstruction formula on the extended limited view data that is given by our proposed approach. Approximation errors of our approach are analyzed. We also present numerical results with the proposed extension approach supporting our theoretical analysis.

A Data-Driven Iteratively Regularized Landweber Iteration

“…This strategy is uneconomical in terms of the amount of usable training data, stability and matrix storage capacity, and this asks for more advanced methods of learning (see for example [1,6]) instead of a linear black-box strategy as a future development. For some literature on deep learning in inverse problems, see for example [1,2,5] and references therein. Looking closer to our proposed algorithm it averages data driven regularization and physical model terms in such a way that in the beginning of the iteration the data driven term is dominant, while during the iteration the physical model takes over the leading role.…”

Deep learning for photoacoustic tomography from sparse data

“…In [44], deep learning is applied to imaging problems where the normal operator is shift invariant; PAT does not belong to this class. A different learning approach for addressing the limited view problem in PAT is proposed in [17]. The above references show that a significant amount of research has been done on deep learning for CT and MRI image reconstruction (based on inverse Radon and inverse Fourier transforms).…”

Compensating unknown speed of sound in learned fast 3D limited-view photoacoustic tomography

“…Model-based learned iterative reconstructions use a network to learn an iterative update including a learned regularisation following conventional model-based iterative methods [67] , [68] , [69] . In addition, neural networks have been used to extend limited-view data to full-view data, allowing artefact reduction when conventional reconstruction methods are utilised [70] .…”