Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bayesian inversion for electromyography using low-rank tensor formats   The reconstruction of the structure of biological tissue using
electromyographic data is a non-invasive imaging method with diverse medical
applications. Mathematically, this process is an inverse problem. Furthermore,
electromyographic data are highly sensitive to changes in the electrical
conductivity that describes the structure of the tissue. Modeling the
inevitable measurement error as a stochastic quantity leads to a Bayesian
approach. Solving the discretized Bayes-inverse problem means drawing samples
from the posterior distribution of parameters, e.g., the conductivity, given
measurement data. Using, e.g., a Metropolis-Hastings algorithm for this purpose
involves solving the forward problem for different parameter combinations which
requires a high computational effort. Low-rank tensor formats can reduce this
effort by providing a data-sparse representation of all occurring linear
systems of equations simultaneously and allow for their efficient solution. The
application of Bayes' theorem proves the well-posedness of the Bayes-inverse
problem. The derivation and proof of a low-rank representation of the forward
problem allow for the precomputation of all solutions of this problem under
certain assumptions, resulting in an efficient and theory-based sampling
algorithm. Numerical experiments support the theoretical results, but also
indicate that a high number of samples is needed to obtain reliable estimates
for the parameters. The Metropolis-Hastings sampling algorithm, using the
precomputed forward solution in a tensor format, draws this high number of
samples and therefore enables solving problems which are infeasible using
classical methods.

13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg