Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Learning The Invisible: A Hybrid Deep Learning-Shearlet Framework for
  Limited Angle Computed Tomography   The high complexity of various inverse problems poses a significant challenge
to model-based reconstruction schemes, which in such situations often reach
their limits. At the same time, we witness an exceptional success of data-based
methodologies such as deep learning. However, in the context of inverse
problems, deep neural networks mostly act as black box routines, used for
instance for a somewhat unspecified removal of artifacts in classical image
reconstructions. In this paper, we will focus on the severely ill-posed inverse
problem of limited angle computed tomography, in which entire boundary sections
are not captured in the measurements. We will develop a hybrid reconstruction
framework that fuses model-based sparse regularization with data-driven deep
learning. Our method is reliable in the sense that we only learn the part that
can provably not be handled by model-based methods, while applying the
theoretically controllable sparse regularization technique to the remaining
parts. Such a decomposition into visible and invisible segments is achieved by
means of the shearlet transform that allows to resolve wavefront sets in the
phase space. Furthermore, this split enables us to assign the clear task of
inferring unknown shearlet coefficients to the neural network and thereby
offering an interpretation of its performance in the context of limited angle
computed tomography. Our numerical experiments show that our algorithm
significantly surpasses both pure model- and more data-based reconstruction
methods.

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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: econ
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga