On the convergence and hyperstability of multidimensional adaptive IIR filtering

A multidimensional version of an adaptive IIR filtering scheme is considered. The scheme can potentially be used for adaptive noise cancellation of multidimensional signals. The authors show that from an analytical standpoint the multidimensional version of the adaptive IIR filtering scheme converges. This result streamlines and greatly simplifies the understanding of previously obtained results for 2-D signals. Also shown is the nontrivial fact that the algorithm can be recursively implemented by exploiting the massive amount of parallelism inherent to it. This fits in exactly with a nonrectangular offset sampling raster previously suggested for processing of multidimensional/video signals in the literature