Inference on binary images from binary data

The problem addressed is to reverse the degradation which occurs when images are digitised: they are blurred, subjected to noise and rounding error, and sampled only at a lattice of points. Inference is considered for the fundamental case of binary scenes, binary data and isotropic blur. The inferential process is separable into two stages: first from the lattice points to a binary image in continuous space and then the reversal of thresholding and blur. Methods are motivated by, and illustrated using, an electron micrograph of an immunogold-labelled section of tulip virus.