Pattern Classification and Reconstruction for Hyperspectral Imagery

In this dissertation, novel techniques for hyperspectral classification and signal reconstruction from random projections are presented. A classification paradigm designed to exploit the rich statistical structure of hyperspectral data is proposed. The proposed framework employs the local Fisher’s discriminant analysis to reduce the dimensionality of the data while preserving its multimodal structure, followed by a subsequent Gaussianmixture- model or support-vector-machine classifier. An extension of this framework in a kernel induced space is also studied. This classification approach employs a maximum likelihood classifier and dimensionality reduction based on a kernel local Fisher’s discriminant analysis. The technique imposes an additional constraint on the kernel mapping—it ensures that neighboring points in the input space stay close-by in the projected subspace. In a typical remote sensing flow, the sender needs to invoke an appropriate compression strategy for downlinking signals (e.g., imagery to a base station). Signal acquisition using random projections significantly decreases the sender-side computational cost, while preserving useful information. In this dissertation, a novel class-dependent hyperspectral image reconstruction strategy is also proposed. The proposed method employs statistics pertinent to each class as opposed to the average statistics estimated over the entire dataset, resulting in a more accurate reconstruction from random projections. An integrated spectral-spatial model for signal reconstruction from random projections is also developed. In this approach, spatially homogeneous segments are combined with spectral pixel-wise classification results in the projected subspace. An appropriate reconstruction strategy, such as compressive projection principal component analysis (CPPCA), is employed individually in each category based on this integrated map. The proposed method provides better reconstruction performance as compared to traditional methods and the class-dependent CPPCA approach