Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Expectation Maximization and the retrieval of the atmospheric extinction
  coefficients by inversion of Raman lidar data   We consider the problem of retrieving the aerosol extinction coefficient from
Raman lidar measurements. This is an ill--posed inverse problem that needs
regularization, and we propose to use the Expectation--Maximization (EM)
algorithm to provide stable solutions. Indeed, EM is an iterative algorithm
that imposes a positivity constraint on the solution, and provides
regularization if iterations are stopped early enough. We describe the
algorithm and propose a stopping criterion inspired by a statistical principle.
We then discuss its properties concerning the spatial resolution. Finally, we
validate the proposed approach by using both synthetic data and experimental
measurements; we compare the reconstructions obtained by EM with those obtained
by the Tikhonov method, by the Levenberg-Marquardt method, as well as those
obtained by combining data smoothing and numerical derivation.

24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int