Feature Extraction via Compressed Local Mahalanobis Metrics

We propose a new energy-based ([1]) online learning approach to the problem of extracting small features from high dimensional, noisy datasets. We demonstrate the power of this new technique by applying it to the Detection of cellular nuclei in large hyperspectral images. Thus, we prove that only a minimum number of random, wideband measurements is necessary to achieve efficient feature extraction of nuclei from the highly structured background. The technology we introduce in our work rests on known results in Compressed Sensing (CS, [2]), a field of study dealing with the task of economically recording information about signals, viewed as elements of a high dimensional vector space V ≃ R , N >> 1. More precisely, CS is a framework developed to allow the reconstruction of discrete signals from few projections onto appropriate Vector Spaces. When attempting to solve a Detection/Estimation problem for a K-sparse 1 set in V ≃ R , where measurments are taken place, we will need M such projections, where: