A Large Scale Parameter Study using kPCA in Hyperspectral Imagery

Undergraduate #67
Discipline: Mathematics and Statistics
Subcategory: Mathematics and Statistics

Michelle Coyle - Claflin University

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Research was conducted involving mathematical techniques for the detection of targets and anomalies in hyperspectral imagery (HSI). HSI is a finer sampling of the light spectrum, sometimes extending beyond the visual range, which results in tens to hundreds of different spectral channels; as compared to normal imagery which has only 3 spectral channels (red, blue, and green). In this high-dimensional space it is difficult, due to the curse-of-dimensionality, to find pixels which are close to a known target or are anomalous when compared to the background. To address the issue, a large scale parameter study was conducted with the use of kernel principal component analysis (kPCA) in order to detect anomalies in HSI. The results of kPCA were compared to the more standard Rx algorithm in regards to its ability to accurately detect anomalies with a low false alarm rate. The results were conveyed through the use of a receiver operating characteristic (ROC) curve, which compares the detection of anomalies to false detection of anomalies. With the use of MATLAB, a program was constructed in order to process through a sub-sample of the data of a HSI, detect anomalies using kPCA, and create a ROC curve from the results. Based on the results of the ROC curve, kPCA proved to be a reasonable method for finding anomalies in HSI. Due to the success of the non-linear kPCA method compared to the linear Rx algorithm method, future research should be conducted to compared the kPCA method to other non-linear methods as well as other HSI.

Funder Acknowledgement(s): U.S. Naval Research Laboratory

Faculty Advisor: Tim Doster, coylemc11@gmail.com

Role: I wrote the code in which the Rx algorithm and the kPCA method was able to be tested in the hyperspectral images. Also, in order to not be computationally limited in the data, I coded a bootstrapping method in which I was able to create synthetic data that accurately mirror the original data. Another problem that I solved in this research was the issue of the methodology being too computationally heavy. In order to make the computation less heavy, I embedded a class system within the code in order to mirror the data while only taking a portion of the original data set. Due to my contributions to this work, the research has been published by SPIE.