625 research outputs found
Deep image prior for 3D magnetic particle imaging: A quantitative comparison of regularization techniques on Open MPI dataset
Magnetic particle imaging (MPI) is an imaging modality exploiting the
nonlinear magnetization behavior of (super-)paramagnetic nanoparticles to
obtain a space- and often also time-dependent concentration of a tracer
consisting of these nanoparticles. MPI has a continuously increasing number of
potential medical applications. One prerequisite for successful performance in
these applications is a proper solution to the image reconstruction problem.
More classical methods from inverse problems theory, as well as novel
approaches from the field of machine learning, have the potential to deliver
high-quality reconstructions in MPI. We investigate a novel reconstruction
approach based on a deep image prior, which builds on representing the solution
by a deep neural network. Novel approaches, as well as variational and
iterative regularization techniques, are compared quantitatively in terms of
peak signal-to-noise ratios and structural similarity indices on the publicly
available Open MPI dataset
Bayesian view on the training of invertible residual networks for solving linear inverse problems
Learning-based methods for inverse problems, adapting to the data's inherent
structure, have become ubiquitous in the last decade. Besides empirical
investigations of their often remarkable performance, an increasing number of
works addresses the issue of theoretical guarantees. Recently, [3] exploited
invertible residual networks (iResNets) to learn provably convergent
regularizations given reasonable assumptions. They enforced these guarantees by
approximating the linear forward operator with an iResNet. Supervised training
on relevant samples introduces data dependency into the approach. An open
question in this context is to which extent the data's inherent structure
influences the training outcome, i.e., the learned reconstruction scheme. Here
we address this delicate interplay of training design and data dependency from
a Bayesian perspective and shed light on opportunities and limitations. We
resolve these limitations by analyzing reconstruction-based training of the
inverses of iResNets, where we show that this optimization strategy introduces
a level of data-dependency that cannot be achieved by approximation training.
We further provide and discuss a series of numerical experiments underpinning
and extending the theoretical findings
Invertible residual networks in the context of regularization theory for linear inverse problems
Learned inverse problem solvers exhibit remarkable performance in
applications like image reconstruction tasks. These data-driven reconstruction
methods often follow a two-step scheme. First, one trains the often neural
network-based reconstruction scheme via a dataset. Second, one applies the
scheme to new measurements to obtain reconstructions. We follow these steps but
parameterize the reconstruction scheme with invertible residual networks
(iResNets). We demonstrate that the invertibility enables investigating the
influence of the training and architecture choices on the resulting
reconstruction scheme. For example, assuming local approximation properties of
the network, we show that these schemes become convergent regularizations. In
addition, the investigations reveal a formal link to the linear regularization
theory of linear inverse problems and provide a nonlinear spectral
regularization for particular architecture classes. On the numerical side, we
investigate the local approximation property of selected trained architectures
and present a series of experiments on the MNIST dataset that underpin and
extend our theoretical findings
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