Distance-Weighted Regularization for Compressed-Sensing Video Recovery and Supervised Hyperspectral Classification

The compressed sensing (CS) model of signal processing, while offering many unique advantages in terms of low-cost sensor design, poses interesting challenges for both signal acquisition and recovery, especially for signals of large size. In this work, we investigate how CS might be applied practically and efficiently in the context of natural video. We make use of a CS video acquisition approach in line with the popular single-pixel camera framework of blind, nonaptive, random sampling while proposing new approaches for the subsequent recovery of the video signal which leverage interrame redundancy to minimize recovery error. We introduce a method of approximation, which we term multihypothesis (MH) frame prediction, to create accurate frame predictions by comparing hypotheses drawn from the spatial domain of chosen reference frames to the non-overlapping, block-by-block CS measurements of subsequent frames. We accomplish this frame prediction via a novel distance-weighted Tikhonov regularization technique. We verify through our experiments that MH frame prediction via distance-weighted regularization provides state-of-the-art performance for the recovery of natural video sequences from blind CS measurements. The distance-weighted regularization we propose need not be limited to just frame prediction for CS video recovery, but may also be used in a variety of contexts where approximations must be generated from a set of hypotheses or training data. To show this, we apply our technique to supervised hyperspectral image (HSI) classification via a novel classifier we term the nearest regularized subspace (NRS) classifier. We show that the distance-weighted regularization used in the NRS method provides greater classification accuracy than state-of-the-art classifiers for supervised HSI classification tasks. We also propose two modifications to the core NRS classifier to improve its robustness to variation of input parameters and and to further increase its classification accuracy