Accelerating Bayesian Computation in Earth Remote Sensing Problems

Abstract

Earth atmospheric remote sensing is an inverse problem that fits surface and atmospheric models to imaging spectrometer data and is critical to the analysis of the composition and biodiversity of the Earth surface. Current methods for remote sensing generally involve retrieving a point estimate of the surface reflectance and atmospheric parameters.

This thesis presents a more robust Bayesian approach to quantify the uncertainty of the retrieval, but this is computationally intractable given the high dimensionality of the problem. In many Bayesian inverse problems, however, there exists a low-dimensional likelihood-informed subspace that describes both optimal projections of the data and directions in parameter space that are most informed by the data.

In the Bayesian approach, Markov chain Monte Carlo (MCMC) is implemented within this low-dimensional subspace to increase sampling efficiency. For an example retrieval, reducing the parameter dimension by a factor of 4 increased the effective sample size of the MCMC chain by more than two orders of magnitude. This low-dimensional subspace was shown to be able to capture the key features of the posterior structure from a higher dimension. The posterior variance obtained through MCMC was also shown to better represent the uncertainty of the problem over the existing method.