Maximum Gaussianity models for hyperspectral images

Peter Bajorski

doi:10.1117/12.778177

11 April 2008 Maximum Gaussianity models for hyperspectral images

Peter Bajorski

Proceedings Volume 6966, Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XIV; 69661M (2008) https://doi.org/10.1117/12.778177
Event: SPIE Defense and Security Symposium, 2008, Orlando, Florida, United States

Abstract

A traditional linear-mixing model with a structured background used in the hyperspectral imaging literature often assumes Gaussianity of the error term. This assumption is often questioned, but to the best of our knowledge, we are not aware of a definite answer on how well such a model may reflect the real hyperspectral images. One difficulty is in the correct identification of the background signatures. The lack of Gaussianity in the error term might be due to missing one of the significant background signatures. In this paper, we investigate this issue using an AVIRIS hyperspectral image. We obtain the projections of the pixel spectra on the orthonormal basis system obtained through the singular value decomposition, and then we measure their Gaussianity using three different methods. We identify the subspace for the structured part of the model based on two criteria - the contribution to the image variability and non-Gaussianity of the marginal distribution. The subspace orthogonal to the structured part of the model forms the subspace of residuals, which is then investigated for multivariate Gaussianity. The resulting model forms a reasonable approximation of the hyperspectral image, and can be successfully used in a variety of applications such as unmixing and target detection. At the same time, it is clear that further improvements are possible by better modeling of the error term distribution.

Citation Download Citation

Peter Bajorski "Maximum Gaussianity models for hyperspectral images", Proc. SPIE 6966, Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XIV, 69661M (11 April 2008); https://doi.org/10.1117/12.778177

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