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| Titel |
Using sparse regularization for multi-resolution tomography of the ionosphere |
| VerfasserIn |
T. Panicciari, N. D. Smith, C. N. Mitchell, F. Dalt, P. S. J. Spencer |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1023-5809
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics ; 22, no. 5 ; Nr. 22, no. 5 (2015-10-19), S.613-624 |
| Datensatznummer |
250121004
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| Publikation (Nr.) |
 copernicus.org/npg-22-613-2015.pdf |
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| Zusammenfassung |
| Computerized ionospheric tomography (CIT) is a technique that allows
reconstructing the state of the ionosphere in terms of electron content from
a set of slant total electron content (STEC) measurements. It is usually
denoted as an inverse problem. In this experiment, the measurements are
considered coming from the phase of the GPS signal and, therefore, affected
by bias. For this reason the STEC cannot be considered in absolute terms but
rather in relative terms. Measurements are collected from receivers not
evenly distributed in space and together with limitations such as angle and
density of the observations, they are the cause of instability in the
operation of inversion. Furthermore, the ionosphere is a dynamic medium whose
processes are continuously changing in time and space. This can affect CIT by
limiting the accuracy in resolving structures and the processes that describe
the ionosphere. Some inversion techniques are based on ℓ2
minimization algorithms (i.e. Tikhonov regularization) and a standard
approach is implemented here using spherical harmonics as a reference to
compare the new method. A new approach is proposed for CIT that aims to
permit sparsity in the reconstruction coefficients by using wavelet basis
functions. It is based on the ℓ1 minimization technique and wavelet
basis functions due to their properties of compact representation. The
ℓ1 minimization is selected because it can optimize the result with
an uneven distribution of observations by exploiting the localization
property of wavelets. Also illustrated is how the inter-frequency biases on
the STEC are calibrated within the operation of inversion, and this is used
as a way for evaluating the accuracy of the method. The technique is
demonstrated using a simulation, showing the advantage of ℓ1
minimization to estimate the coefficients over the ℓ2 minimization.
This is in particular true for an uneven observation geometry and especially
for multi-resolution CIT. |
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