The correction of the influence of phase corrugation in the pupil plane is a fundamental issue in achieving high dynamic range imaging. In this paper, we investigate an instrumental set-up which consists of applying interferometric techniques on a single telescope, by filtering and dividing the pupil with an array of single-mode fibres. We developed a new algorithm, which makes use of the fact that we have a redundant interferometric array, to completely disentangle the astronomical object from the atmospheric perturbations (phase and scintillation). This self-calibrating algorithm can also be applied to any - diluted or not - redundant interferometric set-up. On an 8-m telescope observing at a wavelength of 630 nm, our simulations show that a single-mode pupil remapping system could achieve, at a few resolution elements from the central star, a raw dynamic range up to 10⁶, depending on the brightness of the source. The self-calibration algorithm proved to be very efficient, allowing image reconstruction of faint sources (magnitude = 15) even though the signal-to-noise ratios of individual spatial frequencies are of the order of 0.1. We finally note that the instrument could be more sensitive by combining this set-up with an adaptive optics system. The dynamic range would however be limited by the noise of the small, high-frequency displacements of the deformable mirror.