Replacing pixel representations by point-function schemes for reducing discretization error in ill-posed remote sensing problems,with examples from cloud tomography

Because of their simplicity and low computational cost, discretizations based on pixels have held sway in remote sensing since its inception. Yet functional representations are clearly superior in many applications, for example when combining retrievals from dissimilar remote sensing instruments. Using cloud tomography as an example, this letter shows that a point-function discretization scheme based on linear interpolation can reduce retrieval error of cloud water content up to 40% compared to a conventional pixel scheme. This improvement is particularly marked because cloud tomography, like the vast majority of remote sensing problems, is ill-posed and thus a small inaccuracy in the formulation of the retrieval problem, such as discretization error, can cause a large error in the retrievals.