Derivation and analysis of a computationally efficient discrete Backus-Gilbert footprint-matching algorithm
A computationally efficient discrete Backus-Gilbert (BG) method is derived that is subject to minimization constraints appropriate for footprint-matching applications. The method is flexible, since computational cost can be traded for accuracy. A comparison of the discrete BG method with a non-discrete BG method shows that the new method can be 250% more efficient while maintaining the same accuracy as traditional approaches. In addition, optimization approaches are used to further enhance the computational performance of the discretized BG method. A singular value decomposition approximation is applied that increases the computational efficiencies 43% to 106% while maintaining similar accuracies to the original discretized algorithm. Accuracies of the optimization were found to be scene dependent. In addition, alternative quadrature methods were also tested for several idealized simulated scenes. The results suggest that accuracy improvements could be made using customized quadrature methods that would be employed along known physical data discontinuities (such as along coastlines in microwave imagery data). In addition, regularization behaviors are also discussed; with a particular emphasis on the extension of the method for use with unnormalized gain functions. This work demonstrates that for some gain function configurations local biases can be intrinsic to the system. The flexibility of the discrete BG method allowed for several of the optimizations to be performed in a straightforward manner. Many additional optimizations are likely possible. Due to the lower computational cost of the method, this work is applicable toward applications in which noise may vary dynamically (such as in RFI-contaminated environments). The computational flexibility of the method also makes it well suited to computationally constrained problems such as 4D data assimilation of remote sensing observations.
Microwave remote sensing