The Atomic Force Microscope (AFM) allows the measurement of interactions at interfaces with nanoscale resolution. Imperfections in the shape of the tip often lead to the presence of imaging artefacts such as the blurring and repetition of objects within images. Generally, these artefacts can only be avoided by discarding data and replacing the probe. Under certain circumstances (e.g., rare, high value samples, or extensive chemical/physical tip modification) such an approach is not feasible. Here, we apply a novel deblurring technique, using a Bayesian framework, to yield a reliable estimation of the real surface topography without any prior knowledge of the tip geometry (blind reconstruction). A key contribution is to leverage the significant recently successful body of work in natural image deblurring to solve this problem. We focus specifically on the 'double-tip' effect, where two asperities 1 are present on the tip, each contributing to the image formation mechanism. Finally, we demonstrate that the proposed technique successfully removes the 'double-tip' effect from high resolution AFM images which demonstrate this artefact whilst preserving feature resolution.