Hierarchical deconvolution for incoherent scatter radar data

Abstract

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.

Gaussian process deconvolution

“…Since we have limited information about the source (x can only be known through y as per equation (2.3)), we take a Bayesian approach and impose a prior over x, this prior is a GP. To the best of our knowledge, there is no prior work addressing this setting in conceptual terms from a theoretical perspective, with the exception of a few works that have applied it to specific problems (see [31–35]).…”

“…Though convolutions have largely aided the design of kernels for GPs, contributions in the 'opposite direction', that is, to use the GP toolbox as a means to address the general deconvolution problem, are scarce. To the best of our knowledge, the only attempts to perform Bayesian deconvolution using a GP prior are works that either: focus specifically on detecting magnetic signals from spectropolarimetric observations [31]; only consider discrete-time impulse responses [32]; or, more recently, use an MVN prior for the particular case of a non-stationary Matérn covariance [33], a parameterization proposed by Paciorek & Schervish [34] which has, in particular, been used for scatter radar data [35].…”