A minimum curvature algorithm for tomographic reconstruction of atmospheric chemicals based on optical remote sensing

Abstract

Abstract. Optical remote sensing (ORS) combined with computerized tomography (CT) technique is a powerful tool to retrieve a two-dimensional concentration map over the area under investigation. But unlike the medical CT, the beam number used in ORS-CT is usually dozens comparing to up to hundreds of thousands in the former, which severely limits the spatial resolution and the quality of the reconstructed map. This situation makes the “smoothness” a priori information especially necessary for ORS-CT. Algorithms which produce smooth reconstructions include smooth basis function minimization (SBFM), grid translation and multiple grid (GT-MG), and low third derivative (LTD), among which the LTD algorithm is a promising one with fast speed and simple realization. But its characteristics and the theory basis are not clear. Moreover, the computation efficiency and the reconstruction quality need to be improved for practical applications. This paper employs two theories, i.e., Tikhonov regularization and spatial interpolation, to produce a smooth reconstruction by ORS-CT. Within the two theories’ frameworks, new algorithms can be explored in order to improve the performance. For example, we propose a new minimum curvature (MC) algorithm based on the variational approach in the theory of the spatial interpolation, which reduces the number of linear equations by half comparing to that in the LTD algorithm using the biharmonic equation instead of the smoothness seminorm. We compared our MC algorithm with the non-negative least square (NNLS), GT-MG, and LTD algorithms using multiple test maps. The MC and the LTD algorithms have similar performance on the reconstruction quality. But the MC algorithm needs only about 65\u2009% computation time of the LTD algorithm. It is much simpler in realization than the GT-MG algorithm by using high-resolution grids directly during the reconstruction process to generate a high-resolution map immediately after one reconstruction process is done. Comparing to the traditional NNLS algorithm, it shows better performance in three aspects: (1) the nearness of reconstructed maps is improved by more than 50\u2009%; (2) the peak location accuracy is improved by 1–2\u2009m; and (3) the exposure error is improved by more than 10 times. The testing results show the effectiveness of the new algorithm based on the spatial interpolation theory. Similarly, other algorithms may also be formulated to address problems such as the over-smooth issue in order to further improve the reconstruction equality. The studies will promote the practical application of the ORS-CT mapping of atmospheric chemicals.