Towards unsupervised online band selection in hyperspectral imaging.

Abstract

This thesis explores the problem of unsupervised selection of a set of spectral wavebands in a hyperspectral sensor for a surveillance task. Selecting a subset of wavebands for surveillance has the advantage of reducing data throughput and hence network bandwidth requirements, computational complexity for processing the data and storage requirements in a ground-station. For the sensor designer, Signal-To-Noise Ratio and other sensor-band improvements can be made on those bands deemed critical for the surveillance task. In chapters 3 and 4, we propose the use of locally correlated high-dimensional Gaussian Mixture models to account for band overlap where maximum likelihood estimates of the parameters of such a model are provided using the SAGE-EM (Space Alternating Generalised Expectation Maximisation) algorithm. In both these chapters convex-relaxation strategies are proposed to handle the combinatorial complexity of selecting a subset-of bands that are locally correlated and contain non-Gaussian measurements. However, in chapter 4, we select bands according to anomaly detection criteria as opposed to modelling estimation accuracy (likelihood) as done in chapter 3. We breakdown the problem such that any pixel contains band measurements that belong to either an outlier or partial background distribution, where the distributions diverge across band-subsets in a Kullback-Leibler (KL) divergence sense. A pixel is deemed as an anomaly if it contains a certain number of outliers. We identify the bands that contain the most number of contiguous outlier measurements and also subsequently reveal the presence of anomalies. Finally, in the last chapter we solve the problem of online band selection for sub-pixel compositional hyperspectral models using a Bayesian approach. Online band-selection enables spectral-band cueing and automation for adaptive focal plane arrays where not all bands are used to measure each pixel. We apply beta process models to provide a recursive strategy to select bands based on prior knowledge of their utility as well as bands used in neighbouring pixels. Band utility is measured through convex-relaxation as the subset of bands that provides the best abundance estimation accuracy of training data. The combination of a Gaussian process prior for possible end-members (pure materials) as well as a Gamma distributions for the abundance, enables efficient posterior sampling from a joint Normal-Gamma distribution. Furthermore, natural spectral band variations are retained making the model suitable for band selection, where approximate sum-to-one constraints are enforced through an intelligent update of the Gamma hyperparameters, based on the Dirichelet-Gamma relation. Experiments are conducted on synthetic Gaussian Mixture data with additive noise (Chapters 3, 4), Rochester Institute of Technology (RIT) Target Detection Test using the HyMAP sensor, (Chapter 4), synthetic sub-pixel data created using USGS spectral database [1] (Chapter 4) and AVIRIS-Cuprite dataset used by Mittelman et.al. in [2] (Chapter 4).