Characterization and Reduction of Noise in Manifold Representations of Hyperspectral Imagery

A new workflow to produce dimensionality reduced manifold coordinates based on the improvements of landmark Isometric Mapping (ISOMAP) algorithms using local spectral models is proposed. Manifold space from nonlinear dimensionality reduction better addresses the nonlinearity of the hyperspectral data and often has better per- formance comparing to the results of linear methods such as Minimum Noise Fraction (MNF). The dissertation mainly focuses on using adaptive local spectral models to fur- ther improve the performance of ISOMAP algorithms by addressing local noise issues and perform guided landmark selection and nearest neighborhood construction in local spectral subsets. This work could benefit the performance of common hyperspectral image analysis tasks, such as classification, target detection, etc., but also keep the computational burden low. This work is based on and improves the previous ENH- ISOMAP algorithm in various ways. The workflow is based on a unified local spectral subsetting framework. Embedding spaces in local spectral subsets as local noise models are first proposed and used to perform noise estimation, MNF regression and guided landmark selection in a local sense. Passive and active methods are proposed and ver- ified to select landmarks deliberately to ensure local geometric structure coverage and local noise avoidance. Then, a novel local spectral adaptive method is used to construct the k-nearest neighbor graph. Finally, a global MNF transformation in the manifold space is also introduced to further compress the signal dimensions. The workflow is implemented using C++ with multiple implementation optimizations, including using heterogeneous computing platforms that are available in personal computers. The re- sults are presented and evaluated by Jeffries-Matsushita separability metric, as well as the classification accuracy of supervised classifiers. The proposed workflow shows sig- nificant and stable improvements over the dimensionality reduction performance from traditional MNF and ENH-ISOMAP on various hyperspectral datasets. The computa- tional speed of the proposed implementation is also improved