Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Deblurring of Motionally Averaged Images with Applications to
  Single-Particle Cryo-Electron Microscopy   This paper addresses the deconvolution of an image that has been obtained by
superimposing many copies of an underlying unknown image of interest. The
superposition is assumed to not be exact due to noise, and is described using
an error distribution in position, orientation, or both. We assume that a good
estimate of the error distribution is known. The most natural approach to take
for the purely translational case is to apply the Fourier transform and use the
classical convolution theorem together with a Weiner filter to invert. In the
case of purely rotational deblurring, the similar Fourier analysis is applied.
That is, for an blurred image function defined on polar coordinates, the
Fourier series and the convolution theorem for the series can be applied. In
the case of combinations of translational and rotational errors, the
motion-group Fourier transform is used. In addition, for the three cases we
present the alternative method using Hermite and Laguerre-Fourier expansion,
which has a special property in Fourier transform. The problem that is solved
here is motivated by one of the steps in the cryo-electron-tomographic
reconstruction of biomolecular complexes such as viruses and ion channels.

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The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol