  We develop a new approach for detecting changes in the behavior of stochastic
processes and random fields based on tensor product representations such as the
Karhunen-Lo\`{e}ve expansion. From the associated eigenspaces of the covariance
operator a series of nested function spaces are constructed, allowing detection
of signals lying in orthogonal subspaces. In particular this can succeed even
if the stochastic behavior of the signal changes either in a global or local
sense. A mathematical approach is developed to locate and measure sizes of
extraneous components based on construction of multilevel nested subspaces. We
show examples in $\mathbb{R}$ and on a spherical domain $\mathbb{S}^{2}$.
However, the method is flexible, allowing the detection of orthogonal signals
on general topologies, including spatio-temporal domains.
