Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Inner-Outer Iterative Method for Edge Preservation in Image
  Restoration and Reconstruction   We present a new inner-outer iterative algorithm for edge enhancement in
imaging problems. At each outer iteration, we formulate a Tikhonov-regularized
problem where the penalization is expressed in the 2-norm and involves a
regularization operator designed to improve edge resolution as the outer
iterations progress, through an adaptive process. An efficient hybrid
regularization method is used to project the Tikhonov-regularized problem onto
approximation subspaces of increasing dimensions (inner iterations), while
conveniently choosing the regularization parameter (by applying well-known
techniques, such as the discrepancy principle or the ${\mathcal L}$-curve
criterion, to the projected problem). This procedure results in an automated
algorithm for edge recovery that does not involve regularization parameter
tuning by the user, nor repeated calls to sophisticated optimization
algorithms, and is therefore particularly attractive from a computational point
of view. A key to the success of the new algorithm is the design of the
regularization operator through the use of an adaptive diagonal weighting
matrix that effectively enforces smoothness only where needed. We demonstrate
the value of our approach on applications in X-ray CT image reconstruction and
in image deblurring, and show that it can be computationally much more
attractive than other well-known strategies for edge preservation, while
providing solutions of greater or equal quality.

9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg