An Extension of Augmented Lagrange Multiplier Method for Remote Sensing Inversion
遥感反演中约束最优化方法的拓展

Inversion algorithms are very important in quantitative remote sensing. Currently, the classic least square method is still used widely. We suggest that remote sensing inversions are often typical constrained optimization problems. Many good constrained optimization methods may be used in remote sensing. After a brief review of the constrained optimization methods, we discuss the widely used augmented Lagrange multiplier method in detail. Only one penalty factor is used in this method, even if this factor is not required to be infinitive in theory, it may still increase larger and larger to meet several constraints with very different magnitudes. As a result, similar to the penalty function method, the ill-posed problem and low efficiency still bother the augmented Lagrange multiplier method. As a solution, we extend the penalty factor to be a diagonal penalty matrix, and present an extended augmented Lagrange multiplier method. Because different constraints are given different penalty factors in this new method, a priori knowledge can be used to help decrease the ill-posed problem and increase the iteration speed. After proving this new method in theory, we do detailed simulation and inversion as further validation. It is clear from the statistical analysis that the rate-of-convergence of our method has been improved of about 30 percent compared with the original penalty factor based method but with similar accuracies. Furthermore, it is also found that our extended method is resistant to ill-posed problems.