Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: First order algorithms in variational image processing   Variational methods in imaging are nowadays developing towards a quite
universal and flexible tool, allowing for highly successful approaches on tasks
like denoising, deblurring, inpainting, segmentation, super-resolution,
disparity, and optical flow estimation. The overall structure of such
approaches is of the form ${\cal D}(Ku) + \alpha {\cal R} (u) \rightarrow
\min_u$ ; where the functional ${\cal D}$ is a data fidelity term also
depending on some input data $f$ and measuring the deviation of $Ku$ from such
and ${\cal R}$ is a regularization functional. Moreover $K$ is a (often linear)
forward operator modeling the dependence of data on an underlying image, and
$\alpha$ is a positive regularization parameter. While ${\cal D}$ is often
smooth and (strictly) convex, the current practice almost exclusively uses
nonsmooth regularization functionals. The majority of successful techniques is
using nonsmooth and convex functionals like the total variation and
generalizations thereof or $\ell_1$-norms of coefficients arising from scalar
products with some frame system. The efficient solution of such variational
problems in imaging demands for appropriate algorithms. Taking into account the
specific structure as a sum of two very different terms to be minimized,
splitting algorithms are a quite canonical choice. Consequently this field has
revived the interest in techniques like operator splittings or augmented
Lagrangians. Here we shall provide an overview of methods currently developed
and recent results as well as some computational studies providing a comparison
of different methods and also illustrating their success in applications.

17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn