Robust Principal Component Analysis

LUCINI, MARÍA MAGDALENA; FRERY, ALEJANDRO CESAR

Maceio

Workshop; Teoria da Iinformacao na Analise de Imagens Sar Polarimetricas; 2013

Principal Component Analysis (PCA) is a widely used statistical tool in many image processing applications, such as image classification, temporal change detection and data compression, just to name a few. When dealing with high dimensional data, such as hyperspectral images, its benefits are evident: PCA allows to conveniently reduce the large volume of data and number of variables involved making image visualization and any posterior statistical analysis manageable. However, hyperspectral data present characteristics that may easily corrupt the results of a classical PCA leading to unreliable results. Among those characteristics one can mention the presence of unexpected values that arise mainly due to noisy pixels and background objects whose responses to the sensor are very different from those of their neighbours. These unexpected values are usually masked in the high dimensions of the data. As classical PCA is based on the spectral decomposition of sample covariance or correlation matrices, being these matrices highly sensitive to the presence of atypical values, its use in hyperspectral image processing is not always convenient. We present the advantages of using a robust PCA technique in hyperspectral image compression. To that end we present a brief review of classical and robust PCA procedures before evaluating and comparing their performances when applied to satellite data provided by the hyperspectral sensor AVIRIS (Airborne Visible/Infrared Imaging Spectrometer).