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 mesospheric winter 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.

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.

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