We present a proof of concept for a new algorithm which can be used to detect exoplanets in high contrast images. The algorithm properly combines mutliple observations acquired during different nights, taking into account the orbital motion of the planet. Methods. We simulate SPHERE/IRDIS time series of observations in which we blindly inject planets on random orbits, at random level of S/N, below the detection limit (down to S/N 1.5). We then use an optimization algorithm to guess the orbital parameters, and take into account the orbital motion to properly recombine the different images, and eventually detect the planets. We show that an optimization algorithm can indeed be used to find undetected planets in temporal sequences of images, even if they are spread over orbital time scales. As expected, the typical gain in S/N ratio is sqrt(n), n being the number of observations combined. We find that the K-Stacker algorithm is able de-orbit and combine the images to reach a level of performance similar to what could be expected if the planet was not moving. We find recovery rates of 50% at S/N=5. We also find that the algorithm is able to determine the position of the planet in individual frames at one pixel precision, even despite the fact that the planet itself is below the detection limit in each frame. Our simulations show that K-Stacker can be used to increase the contrast limit of current exoplanet imaging instruments and to discover fainter bodies. We also suggest that the ability of K-Stacker to determine the position of the planet in every image of the time serie could be used as part of a new observing strategy in which long exposures would be broken into shorter ones spread over months. This could make possible to determine the orbital parameters of a planet without requiring multiple high S/N > 5 detections.
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