A Regularization-based Tomographic Reconstruction Algorithm for Horizontal Radial Plume Mapping of Trace Gases

Computed tomography optical remote sensing (CT-ORS) is a powerful tool to retrieve the two-dimensional concentration map of trace gases over a large area under investigation. Horizontal radial plume mapping (HRPM) is easy to be deployed in practice by using only one detector and a non-overlapped beam geometry. But the reconstruction task is more difficult than that using the overlapped beam geometry. The pixel-based reconstruction method of non-negative least square (NNLS) performs poorly in HRPM configuration due to the fixed coarse grid resolution, especially under the conditions when the peak locations of the concentration are near to the detector. We have developed a new algorithm based on grid interpolation and regularization techniques. First, the original grids determined by the HRPM configuration were interpolated into high-resolution grids before the reconstruction. Then, the generated highly underdetermined system of linear equations was regularized using low third derivatives (LTD) approach, resulting in an overdetermined system of linear equations. Finally, the NNLS algorithm was used to find the least square solution. To compare the performances between the new algorithm and traditional NNLS algorithm, multiple distribution maps were generated using bivariate Gaussian distribution, bivariate lognormal distribution, and Gaussian dispersion model. Results under these different distribution conditions showed that the new method significantly improved the accuracy of the reconstruction, especially the accuracy of the peak location. This new algorithm is fast and accurate by taking advantages of both the fast computation of NNLS algorithm and the smoothness solution of smooth basis function minimization (SBFM) algorithm. It is expected to promote the actual application of the CT-ORS mapping of air pollutants.