  Performing likelihood ratio based detection with high dimensional multimodal
data is a challenging problem since the computation of the joint probability
density functions (pdfs) in the presence of inter-modal dependence is
difficult. While some computationally expensive approaches have been proposed
for dependent multimodal data fusion (e.g., based on copula theory), a commonly
used tractable approach is to compute the joint pdf as the product of marginal
pdfs ignoring dependence. However, this method leads to poor performance when
the data is strongly dependent. In this paper, we consider the problem of
detection when dependence among multimodal data is modeled in a compressed
domain where compression is obtained using low dimensional random projections.
We employ a Gaussian approximation while modeling inter-modal dependence in the
compressed domain which is computationally more efficient. We show that, under
certain conditions, detection with multimodal dependent data in the compressed
domain with a small number of compressed measurements yields enhanced
performance compared to detection with high dimensional data via either the
product approach or other suboptimal fusion approaches proposed in the
literature.
