Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficient generalized Golub-Kahan based methods for dynamic inverse
  problems   We consider efficient methods for computing solutions to and estimating
uncertainties in dynamic inverse problems, where the parameters of interest may
change during the measurement procedure. Compared to static inverse problems,
incorporating prior information in both space and time in a Bayesian framework
can become computationally intensive, in part, due to the large number of
unknown parameters. In these problems, explicit computation of the square root
and/or inverse of the prior covariance matrix is not possible. In this work, we
develop efficient, iterative, matrix-free methods based on the generalized
Golub-Kahan bidiagonalization that allow automatic regularization parameter and
variance estimation. We demonstrate that these methods can be more flexible
than standard methods and develop efficient implementations that can exploit
structure in the prior, as well as possible structure in the forward model.
Numerical examples from photoacoustic tomography, deblurring, and passive
seismic tomography demonstrate the range of applicability and effectiveness of
the described approaches. Specifically, in passive seismic tomography, we
demonstrate our approach on both synthetic and real data. To demonstrate the
scalability of our algorithm, we solve a dynamic inverse problem with
approximately $43,000$ measurements and $7.8$ million unknowns in under $40$
seconds on a standard desktop.

31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an