  We introduce a new framework for point-spread function (PSF) subtraction
based on the spatio-temporal variation of speckle noise in high-contrast
imaging data where the sampling timescale is faster than the speckle evolution
timescale. One way that space-time covariance arises in the pupil is as
atmospheric layers translate across the telescope aperture and create small,
time-varying perturbations in the phase of the incoming wavefront. The
propagation of this field to the focal plane preserves some of that space-time
covariance. To utilize this covariance, our new approach uses a
Karhunen-Lo\'eve transform on an image sequence, as opposed to a set of single
reference images as in previous applications of Karhunen-Lo\'eve Image
Processing (KLIP) for high-contrast imaging. With the recent development of
photon-counting detectors, such as microwave kinetic inductance detectors
(MKIDs), this technique now has the potential to improve contrast when used as
a post-processing step. Preliminary testing on simulated data shows this
technique can improve contrast by at least 10-20% from the original image, with
significant potential for further improvement. For certain choices of
parameters, this algorithm may provide larger contrast gains than spatial-only
KLIP.
