Recovering images from partial information using Δ2G filtering

The recovery of an image from partial information through the use of Δ²G filtering is discussed. A technique is developed for the recovery of a Δ²G filtered image from partial information, based only on contrast figure estimates taken at the sampled Δ²G filtered image zero crossings. A practical method is developed for estimating an edge contrast figure at each zero-crossing sample and for recovering the Δ²G filtered image from these zero-crossing sample values. This technique does not involve the solution of simultaneous equations, and therefore avoids the numerical problems often faced with such an approach. Further, this technique does not involve iteration, and therefore avoids the convergence problems and large number of computations often incurred by techniques which use iteration. Good image reconstruction is demonstrated, with the zero-crossing samples localized only to the original image sample grid