On Constructing Minimal Ghosts

Ghosts are digital images that contain highly constrained patterns of signed pixel values. The pixels are located so as to create zero-sums when discrete projections are taken across the image at a pre-determined set of angles. Ghosts can be applied to create image/anti-image pairs. An image that is entangled with its anti-image can be used to achieve forward error-correction in redundant data transmission schemes. Ghosts can also be used to help reconstruct images from asymmetric sets of real, noisy tomographic projection data. Minimal ghosts do these tasks most efficiently. We present here new methods to construct minimal ghost images that employ just 2N pixels to obtain zero-sum projections for N angles. Construction of an Nth order ghost had previously required O(2^N) pixels.