Using sparse regularization for multi-resolution tomography of the ionosphere
Using sparse regularization for multi-resolution tomography of the ionosphere
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DOI：
10.5194/npg-22-613-2015
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发表时间：
2015-01-01
影响因子：
2.2
通讯作者：
Spencer, P. S. J.
中科院分区：
文献类型：
--
作者：
Panicciari, T.;Smith, N. D.;Spencer, P. S. J.
计算机电离层层析成像（CIT）是一种技术，它允许从一组倾斜总电子含量（STEC）测量中重建电离层的电子含量状态。它通常被称为逆问题。在本实验中，测量值被认为来自GPS信号的相位，因此受到偏差的影响。因此，不能从绝对的角度来考虑STEC，而应从相对的角度来考虑STEC。测量值是从空间分布不均匀的接收器收集的，再加上观测角度和密度等限制，它们是反演操作不稳定的原因。此外，电离层是一种动态介质，其过程在时间和空间上不断变化。这可能会通过限制解析电离层结构和描述电离层过程的准确性来影响CIT。一些反演技术基于l（2）最小化算法（即Tikhonov正则化），并且这里使用球面谐波作为参考来实现标准方法以比较新方法。提出了一种新的方法，CIT的目的是允许稀疏的重构系数，通过使用小波基函数。它是基于l（1）最小化技术和小波基函数，由于其性质的紧凑表示。选择l（1）最小化是因为它可以利用小波的局部化特性，在观测值分布不均匀的情况下优化结果。还示出了如何在反演操作内校准STEC上的频率间偏差，并且这被用作评估该方法的精度的一种方式。该技术是使用模拟演示，显示的优势，l（1）最小化估计的系数超过l（2）最小化。这对于不均匀的观测几何形状尤其是对于多分辨率CIT尤其如此。
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 l(2) 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 l(1) minimization technique and wavelet basis functions due to their properties of compact representation. The l(1) 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 l(1) minimization to estimate the coefficients over the l(2) minimization. This is in particular true for an uneven observation geometry and especially for multi-resolution CIT.