Inversion of remote sensing data in a shallow water environment using a trans-dimensional probabilistic framework
Creators: name: Sagar, Stephen
Publisher: name: The Australian National University
Year: 2015
Subjects: subject: Remote sensing Research
subject: Hydrology Statistical methods
subject: Ocean bottom Remote sensing
subject: Oceanography Remote sensing
subject: Lee Stocking Island (Bahamas)

description: Image data from remote sensing platforms offer an opportunity to observe and monitor the physical environment at a scale and precision unavailable to previous generations. The ability to estimate environmental parameters in a range of terrestrial and aquatic scenarios, often in remote and inaccessible areas, is a key benefit of using remote sensing data. Estimating physical parameters from remote sensing data takes the form of an inverse problem, predominately tackled using single solution optimisation approaches applied on a pixel-by-pixel basis. These types of inversion methods are poorly suited to the non-uniqueness that characterises many of the physical models in remote sensing, and often require some form of subjective regularisation to produce sensible estimates and parameter combinations. In this thesis the inversion of remote sensing data is cast in a probabilistic framework, with the first application of a trans-dimensional sampling algorithm to this form of problem. Probabilistic sampling techniques offer considerable benefits in term of encompassing uncertainties in both the model and the data, and provide an ensemble of solutions from which parameter estimates and uncertainties can be inferred. However, probabilistic sampling has not been widely applied to remote sensing image data, primarily due to the high dimension of the data and inverse problem. Using a physical model for a shallow water environment, we demonstrate the application of a spatially partitioned reverse jump Markov chain Monte Carlo (rj-McMC) algorithm, previously developed for geophysical applications where the dimension of the inverse problem is treated as unknown. To effectively deal with the increased dimension of the remote sensing problem, a new version of the algorithm is developed in this thesis, utilising image segmentation techniques to guide the dimensional changes in the rj-McMC sampling process. Synthetic data experiments show that the segment guided component of the algorithm is essential to sample the high dimensions of a complex spatial environment such as a coral reef. As the complexity of the data and forward model is increased, further innovations to the algorithm are introduced. These include, enabling the estimation of data noise as part of the inversion process, and the use of the segmentation to develop informed starting points for the initial parameters in the model. The original algorithm developed in this thesis is then applied to a hyperspectral remote sensing problem in the coral waters of Lee Stocking Island, Bahamas. The algorithm is shown to produce an estimated depth model of increased accuracy in comparison to a range of optimisation inversion methods applied at this study site. The self-regularisation of the partition modelling approach proves effective in minimising the pixel-to-pixel variation in the depth solution, whilst maintaining the fine-scale spatial discontinuities of the coral reef environment. Importantly, inferring a depth model from an ensemble of solutions, rather than a single solution, enables uncertainty to be attributed to the model parameters. This is a crucial step in integrating bathymetry information estimated from remote sensing data with other traditional surveying methods.