  High-contrast imaging surveys for exoplanet detection have shown giant
planets at large separations to be rare. It is important to push towards
detections at smaller separations, the part of the parameter space containing
most planets. The performance of traditional methods for post-processing of
pupil-stabilized observations decreases at smaller separations, due to the
larger field-rotation required to displace a source on the detector in addition
to the intrinsic difficulty of higher stellar contamination. We developed a
method of extracting exoplanet signals that improves performance at small
angular separations. A data-driven model of the temporal behavior of the
systematics for each pixel can be created using reference pixels at a different
position, assuming the underlying causes of the systematics are shared across
multiple pixels. This is mostly true for the speckle pattern in high-contrast
imaging. In our causal regression model, we simultaneously fit the model of a
planet signal "transiting" over detector pixels and non-local reference
lightcurves describing a basis of shared temporal trends of the speckle pattern
to find the best fitting temporal model describing the signal. With our
implementation of a spatially non-local, temporal systematics model, called
TRAP, we show that it is possible to gain up to a factor of 6 in contrast at
close separations ($<3\lambda/D$) compared to a model based on spatial
correlations between images displaced in time. We show that better temporal
sampling resulting in significantly better contrasts. At short integration
times for $\beta$ Pic data, we increase the SNR of the planet by a factor of 4
compared to the spatial systematics model. Finally, we show that the temporal
model can be used on unaligned data which has only been dark and flat
corrected, without the need for further pre-processing.
