Quantisation Invariants for Transform Parameter Estimation in Coding Chains

We examine the case of a signal going through a processing chain consisting of two transform coding stages, with the aim of recovering the unknown parameters of the first encoder. Through number theoretical considerations, we identify a lattice of quantisation invariant points, whose coordinates are not affected by the double quantisation and whose parameters are closely related to the unknown transform. The conditions for this lattice to exist are then discussed, and its uniqueness properties analysed. Finally, an algorithmic procedure to recover the invariants from a sparse set of points is shown together with numerical results.