On the Determination of All the Sublattices of Preassigned Index and Its Application to Multidimensional Subsampling

Subsampling offers an effective and simple way to implement a data compression technique. Its use in the video context is rather attractive, as its application to current video broadcasting schemes, such as MUSE and HD-MAC, clearly shows. A sensible exploitation of subsampling's potential requires the systematic evaluation of the image degradation effects due to the specific subsampling lattice. Such a possibility is equivalent to the determination of all the sublattices of a given index within a lattice, a problem that can be solved, as the work shows, on the basis of the Hermite normal-form theorem. The practical use of the result in the subsampling context is exemplified for a data compression case.