  Quickest change point detection is concerned with the detection of
statistical change(s) in sequences while minimizing the detection delay subject
to false alarm constraints. In this paper, the problem of change point
detection is studied when the decision maker only has access to compressive
measurements. First, an expression for the average detection delay of
Shiryaev's procedure with compressive measurements is derived in the asymptotic
regime where the probability of false alarm goes to zero. Second, the
dependence of the delay on the compression ratio and the signal to noise ratio
is explicitly quantified. The ratio of delays with and without compression is
studied under various sensing matrix constructions, including Gaussian
ensembles and random projections. For a target ratio of the delays after and
before compression, a sufficient condition on the number of measurements
required to meet this objective with prespecified probability is derived.
