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- Title
Using sparse regularization for multi-resolution tomography of the ionosphere.
- Authors
Panicciari, T.; Smith, N. D.; Mitchell, C. N.; Da Dalt, F.; Spencer, P. S. J.
- Abstract
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 insta-bility 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 l1 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.
- Subjects
IONOSPHERE; MATHEMATICAL regularization; COMPUTED tomography; IMAGE reconstruction; TOTAL electron content (Atmosphere); COEFFICIENTS (Statistics); ACQUISITION of data
- Publication
Climate of the Past Discussions, 2015, p613
- ISSN
1814-9324
- Publication type
Article
- DOI
10.5194/npg-22-613-2015