Regularization for inverse models in remote sensing

Quantitative remote sensing is an appropriate way to estimate atmospheric parameters and structural parameters and spectral component signatures of Earth surface cover type. Since the real physical system that couples the atmosphere, water and the land surface is complicated, its description requires a comprehensive set of parameters, so any practical physical model can only be approximated by a limited mathematical model. The pivotal problem for quantitative remote sensing is inversion. Inverse problems are typically ill-posed; they are characterized by: (C-1) the solution may not exist; (C-2) the dimension of the solution space may be infinite; (C-3) the solution is not continuous with variations of the observations. These issues exist for nearly all inverse problems in geosciences and quantitative remote sensing. For example, when the observation system is band-limited or sampling is poor, i.e. few observations are available or directions are poorly located, the inversion process would be underdetermined, which leads to a multiplicity of the solutions, the large condition number of the normalized system, and significant noise propagation. Hence (C-2) and (C-3) would be the difficulties for quantitative remote sensing inversion. This paper will address the theory and methods from the viewpoint that the quantitative remote sensing inverse problems can be represented by kernel-based operator equations and solved by coupling regularization and optimization methods. In particular, I propose sparse and non-smooth regularization and optimization techniques for solving inverse problems in remote sensing. Numerical experiments are also made to demonstrate the applicability of our algorithms.