Our research group is partly responsible (with Christian Marois) for the first direct imaging of a new planetary system around the star HR 8799. There are two main reasons which permit such an exploit ;
This is where the LOCI algorithm kicks in. The trick is to take a small portion of one single exposure and then try to build the speckle pattern in this small region. To do this, we use a linear combination of the same region in all other relevant exposures. We then ask that the subtraction of this reconstructed speckle pattern to the initial region of interests leaves the least signal possible in it -- this is done by asking that the variance of the pixels in the region is the closest possible to zero. It is then possible to write down this criteria as a linear system of equations, from which the inversion reveals the best coefficients to build the speckle pattern from other exposures. Once this calculation is completed, the subtraction of the initial region with this synthetic speckle pattern would reveal any planet for which the contrast with its host star is sufficiently high. This happens since the physical signal of the planet has gone into another region because of rotation between frames, which prevents the linear combination to reconstruct this signal. Hence, the subtraction doesn't remove the planet which was hidden in the host star's halo of speckles.
However, even if this method doesn't completely subtract the signal of hidden exoplanets, it is quite aggressive in the sense it does affect it in a way which is hard to calibrate. Our team is currently working in collaboration with Jérôme Maire on an update to this algorithm which would let the planet's flux significantly less affected.
This method permitted the detection of HR 8799's three outermost planets in old NICMOS data from 1998 - which means if LOCI was already developed back then, we could have already found this planetary system !