Mapping of Post-Disaster Environments using 3D Backprojection and Iterative Inversion Methods Optimised for Limited-Pixel Gamma Spectrometers on Unoccupied Aerial Systems (UAS).&#160;
Authors: Connor Dean , Megson-Smith David , Wood Kieran , Mackenzie Robbie , Connolly Euan , White Sam , Russell-Pavier Freddie , Ryan-Tucker Matthew , Martin Peter , Verbelen Yannick , Richardson Thomas , Smith Nick , Scott Thomas 
Published: March 2022

&lt;p&gt;All radiological measurements acquired from airborne detectors suffer from the issues of geometrical signal dilution, signal attenuation and a complex interaction of the effective sampling area of the detector system with the 3D structure of the surrounding environment. Understanding and accounting for these variables is essential in recovering accurate dose rate maps that can help protect responding workforces in radiologically contaminated environments.&lt;/p&gt;&lt;p&gt;Two types of terrain-cognisant methods of improving source localisation and the contrast of airborne radiation maps are presented in this work, comprising of &amp;#8216;Point Cloud Constrained 3D Backprojection&amp;#8217; and &amp;#8216;Point Cloud Constrained Randomised Kaczmarz Inversion&amp;#8217;. Each algorithm uses a combination of airborne gamma-spectrometry and 3D scene information collected by UAS platforms and have been applied to data collected with lightweight, simple (non-imaging) detector payloads at numerous locations across the Chornobyl Exclusion Zone (CEZ).&lt;/p&gt;&lt;p&gt;Common to both the algorithms is the projection of the photopeak intensity onto a point cloud representation of the environment, taking into account the position and orientation of the UAS in addition to the 3D response of the spectrometer. The 3D Backprojection method can be considered a relatively fast method of mapping of through proximity, in which the measured photopeak intensity is split over the point cloud according to the above factors. It is an additive technique, with each measurement increasing the overall magnitude of the radiation field assigned to the survey area, meaning that more measurements continues to increase the total radiation of the site. The total measured intensity of the solution is then normalised according to the time spent in proximity to each point in the scene, determined by splitting and projecting the nominal measurement time at each survey point over the point cloud according to the distance from the survey position. Thus accounting for sampling biases during the survey.&lt;/p&gt;&lt;p&gt;The inversion approach adapts algorithms routinely used in medical imaging for the unconstrained world in which the detector is no longer completely surrounding the subject/target. A forward projection model, based on the contribution of distant point sources to the detector intensity, is used to determine the relationship between the full set of measurements and the 3D scene. This results in a hypercube of linear equations where it is assumed every point in the scene contributes to the measured intensity. The algorithm randomly adds measurements from within the aerial set and back-projects this onto the point cloud, with the initial state of the solution set to emit no radiation. After a given number of iterations, the fit of the current solution to the original measurements is assessed though a least squares method and updated when this produces a fit better than the current best estimate. This continues to happen until a minimum value is reached before the divergence of the system, representing the most confident solution. Based on examples from both simulations and real world data, the improvement in contrast of airborne maps using this inversion method can make them equivalent to ground-based surveys, even when operating at 20 m AGL and above.&lt;/p&gt;