Comparison and Usage of Principal Component Analysis (PCA) and Noise Adjusted Principal Component (NAPC) Analysis or Maximum Noise Fraction (MNF) Emmett J. Ientilucci Chester F. Carlson Center for Imaging Science Rochester Institute of Technology 54 Lomb Memorial Drive Rochester, NY 14623-5604 emmett@cis.rit.edu May 6, 2003 Abstract A detailed theoretical basis on principal components and noise adjusted principal component transforms is presented. Both algorithms are applied to multispectral im- agery collected with the (RIT) MISI airborne imaging system. Approaches for reducing both dimensionality and noise contributions are presented. Analysis is made by com- paring and contrasting each technique as applied to a specific application area. 1 Introduction Principal component analysis (PCA) is a very powerful tool for analyzing multi and hyper- spectral imagery. For example, PCA can be used to exploit the redundancy or correlation in a data set by reducing the inherent dimensionality. Additionally it can be used as a means of reducing the noise contribution in an image. Along these lines, a modified version of the PC transform called the noise adjusted principal component (NAPC) transform can be used to further separate noise from relevant image information. This report presents the theoretical background of both algorithms. In addition, the algorithms are implemented on multispectral imagery while simultaneously reducing both dimensionality and noise contributions. 2 Multispectral Data Set The multispectral data set that was used for this analysis came from the Modular Imaging Spectrometer Instrument (MISI). The data set under test was an image of the Lake Ontario shoreline near Russell Station located in Rochester, NY. The data was collected on September 9, 2001. The MISI instrument was flown at an altitude of 5000 feet with a ground speed of 128 knots. A roll corrected visible sub-sectioned image is seen in Figure 1a while the (uncorrected) NIR band is shown in Figure 1b. Figure 2 shows each of the sixteen (16) NIR bands (730 nm to 985 nm) from the spec- trometer. Below each image is the total variance for that particular band (in digital counts). Each image has been linearly scaled by the same amount. Doing so illustrates the lack of 1