Three-dimensional Lossless Compression Based on a Separable Generalized Recursive Interpolation

In this work, it is shown that the generalized recursive interpolation (GRINT) proposed is the most effective progressive technique for inter-frame reversible compression of tomographic sections that typically occur in the medical field. An image sequence is decimated by a factor 2, first along rows only, then along columns only, and eventually along slices only, recursively in a sequel, thus creating a gray-level hyperpyramid whose number of voxels halves at every level. The top of the pyramid (root) is stored and then directionally interpolated by means of a 1D kernel. Interpolation errors with the underlying equally-sized hyperlayer are stored as well. The same procedure is repeated, until the image sequence is completely decomposed. The advantage of the novel scheme with respect to other noncausal DPCM schemes is twofold: firstly interpolation is performed from all error-free values, thereby reducing the variance of residuals; secondly different correlation values along rows, columns and sections can be exploited for a better decorrelation.