Abstract. We propose a novel method for deconvolving incoherent scatter radar data to recover accurate reconstructions of backscattered powers. The problem is modelled as a hierarchical noise-perturbed deconvolution problem, where the lower hierarchy consists of an adaptive length-scale function that allows for a non-stationary prior and as such enables adaptive recovery of smooth and narrow layers in the profiles. The estimation is done in a Bayesian statistical inversion framework as a two-step procedure, where hyperparameters are first estimated by optimisation and followed by an analytical closed-form solution of the deconvolved signal. The proposed optimisation based method is compared to a fully probabilistic approach using Markov Chain Monte Carlo techniques enabling additional uncertainty quantification. In this paper we examine the potential of the hierarchical deconvolution approach using two different prior models for the length-scale function.We apply the developed methodology to compute the backscattered powers of measured Polar MesosphericWinter Echoes, as well as Summer Echoes, from the EISCAT VHF radar in Tromsø, Norway. Computational accuracy and performance are tested using a simulated signal corresponding to a typical background ionosphere and a sporadic E layer with known ground-truth. The results suggest that the proposed hierarchical deconvolution approach can recover accurate and clean reconstructions of profiles, and the potential to be successfully applied to similar problems.

中文翻译：

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非相干散射雷达数据的分层解卷积

摘要。我们提出了一种去卷积非相干散射雷达数据的新方法，以恢复反向散射功率的准确重建。该问题被建模为分层噪声扰动解卷积问题，其中较低的层次结构由自适应长度尺度函数组成，该函数允许非平稳先验，因此能够自适应恢复轮廓中的平滑和窄层。估计是在贝叶斯统计反演框架中作为两步过程完成的，其中首先通过优化估计超参数，然后是解卷积信号的解析封闭形式解。将所提出的基于优化的方法与使用马尔可夫链蒙特卡罗技术的完全概率方法进行比较，从而实现额外的不确定性量化。在本文中，我们使用两种不同的长度尺度函数先验模型来检验分层解卷积方法的潜力。挪威特罗姆瑟的雷达。使用对应于典型背景电离层和具有已知地面实况的零星 E 层的模拟信号来测试计算精度和性能。结果表明，所提出的 使用对应于典型背景电离层和具有已知地面实况的零星 E 层的模拟信号来测试计算精度和性能。结果表明，所提出的 使用对应于典型背景电离层和具有已知地面实况的零星 E 层的模拟信号来测试计算精度和性能。结果表明，所提出的分层解卷积方法可以恢复轮廓的准确和干净的重建，以及成功应用于类似问题的潜力。