Computerized ionospheric tomography (CIT) is an ill-posed inverse problem owing to insufficient data acquisition. Therefore, the ionospheric electron density (IED) distributions cannot be reconstructed accurately. Although many attempts have been made to deal with this issue, there is still a long way to go before it can be completely overcome. Specifically, the inverted IEDs of voxels without observational information show a strong dependence on initial values, which affects the overall accuracy of CIT. Taking this into account, a new three-dimensional CIT model is developed, based on a backpropagation neural network. The neural network model is trained using the characteristics and inverted IEDs of voxels with observational information, and then, the IEDs of voxels without observational information are predicted again. Careful validation of the proposed model is performed by conducting numerical experiments with GPS simulation and real data under both quiet and disturbed ionospheric conditions. Compared with the traditional non-neural network method in the simulation experiment, the proposed method offers improvements of 62.0 and 56.89% in root mean square error and the mean absolute error for those voxels without observational information, respectively, while it offers improvements of 30.98 and 26.67% for all voxels of the whole region. In the real data experiment, the IEDs of the control groups obtained by the proposed method are compared with the target IEDs for all periods. The result presents correlation coefficient greater than 0.96 between this predicted IEDs and the target IEDs for all periods, and this further certifies the feasibility of the proposed method. Additionally, the latitude–longitude maps and profiles of the ionospheric electron density also show that the ill-posedness problem has a significantly weaker effect for those voxels without observational information.

由于数据采集不足，电离层层析成像（CIT）是一个不适当地的逆问题。因此，电离层电子密度（IED）分布不能准确地重建。尽管已为解决此问题进行了许多尝试，但要完全克服它还有很长的路要走。具体来说，没有观测信息的体素的倒置IED显示出对初始值的强烈依赖性，这会影响CIT的整体准确性。考虑到这一点，基于反向传播神经网络，开发了一个新的三维CIT模型。利用具有观测信息的体素的特征和倒置IED训练神经网络模型，然后再次预测没有观测信息的体素的IED。通过在安静和受干扰的电离层条件下，利用GPS模拟和实际数据进行数值实验，可以对所提出的模型进行仔细验证。与模拟实验中的传统非神经网络方法相比，该方法对没有观测信息的体素的均方根误差和平均绝对误差分别提高了62.0％和56.89％，而对均值的改进分别为30.98和56.89％。整个区域中所有体素的26.67％。在实际数据实验中，将通过所提出的方法获得的对照组的IED与所有时期的目标IED进行比较。结果表明，在所有期间内，此预测IED与目标IED之间的相关系数均大于0.96，这进一步证明了该方法的可行性。另外，电离层电子密度的纬度-经度图和剖面图也表明，不适定性问题对那些没有观测信息的体素的影响明显减弱。