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 ($<3lambda/D$) 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.
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