Title: Compressive Sensing-Based Detection with Multimodal Dependent Data,
Abstract: Detection with high dimensional multimodal data is a challenging problem when
there are complex inter- and intra- modal dependencies. While several
approaches have been proposed for dependent data fusion (e.g., based on copula
theory), their advantages come at a high price in terms of computational
complexity. In this paper, we treat the detection problem with compressive
sensing (CS) where compression at each sensor is achieved via low dimensional
random projections. CS has recently been exploited to solve detection problems
under various assumptions on the signals of interest, however, its potential
for dependent data fusion has not been explored adequately. We exploit the
capability of CS to capture statistical properties of uncompressed data in
order to compute decision statistics for detection in the compressed domain.
First, a Gaussian approximation is employed to perform likelihood ratio (LR)
based detection with compressed data. In this approach, inter-modal dependence
is captured via a compressed version of the covariance matrix of the
concatenated (temporally and spatially) uncompressed data vector. We show that,
under certain conditions, this approach with a small number of compressed
measurements per node leads to enhanced performance compared to detection with
uncompressed data using widely considered suboptimal approaches. Second, we
develop a nonparametric approach where a decision statistic based on the second
order statistics of uncompressed data is computed in the compressed domain. The
second approach is promising over other related nonparametric approaches and
the first approach when multimodal data is highly correlated at the expense of
slightly increased computational complexity.