544 research outputs found
Approximate k-space models and Deep Learning for fast photoacoustic reconstruction
We present a framework for accelerated iterative reconstructions using a fast
and approximate forward model that is based on k-space methods for
photoacoustic tomography. The approximate model introduces aliasing artefacts
in the gradient information for the iterative reconstruction, but these
artefacts are highly structured and we can train a CNN that can use the
approximate information to perform an iterative reconstruction. We show
feasibility of the method for human in-vivo measurements in a limited-view
geometry. The proposed method is able to produce superior results to total
variation reconstructions with a speed-up of 32 times
Fourier Neural Operator Networks: A Fast and General Solver for the Photoacoustic Wave Equation
Simulation tools for photoacoustic wave propagation have played a key role in
advancing photoacoustic imaging by providing quantitative and qualitative
insights into parameters affecting image quality. Classical methods for
numerically solving the photoacoustic wave equation relies on a fine
discretization of space and can become computationally expensive for large
computational grids. In this work, we apply Fourier Neural Operator (FNO)
networks as a fast data-driven deep learning method for solving the 2D
photoacoustic wave equation in a homogeneous medium. Comparisons between the
FNO network and pseudo-spectral time domain approach demonstrated that the FNO
network generated comparable simulations with small errors and was several
orders of magnitude faster. Moreover, the FNO network was generalizable and can
generate simulations not observed in the training data
On Learned Operator Correction in Inverse Problems
We discuss the possibility of learning a data-driven explicit model correction for inverse problems and whether such a model correction can be used within a variational framework to obtain regularized reconstructions. This paper discusses the conceptual difficulty of learning such a forward model correction and proceeds to present a possible solution as a forward-adjoint correction that explicitly corrects in both data and solution spaces. We then derive conditions under which solutions to the variational problem with a learned correction converge to solutions obtained with the correct operator. The proposed approach is evaluated on an application to limited view photoacoustic tomography and compared to the established framework of the Bayesian approximation error method
Inverse Problems with Learned Forward Operators
Solving inverse problems requires knowledge of the forward operator, but accurate models can be computationally expensive and hence cheaper variants are desired that do not compromise reconstruction quality. This chapter reviews reconstruction methods in inverse problems with learned forward operators that follow two different paradigms. The first one is completely agnostic to the forward operator and learns its restriction to the subspace spanned by the training data. The framework of regularisation by projection is then used to find a reconstruction. The second one uses a simplified model of the physics of the measurement process and only relies on the training data to learn a model correction. We present the theory of these two approaches and compare them numerically. A common theme emerges: both methods require, or at least benefit from, training data not only for the forward operator, but also for its adjoint
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