Image filtering using hyperstable adaptive algorithms

In view of recent interest in applications of adaptive filtering of multidimensional (m-D) signals in practical problems such as video compression and image enhancement, implementation of a class of m-D infinite impulse response, adaptive, hyperstable filters is undertaken. While the theoretical results on convergence of such schemes have been made available in our recent work on the topic, the present paper reports our experiments with enhancement of noise-corrupted images for the first time. Aside from implementing the previously introduced m-D HARF algorithm, we also introduce and implement other variants of the algorithm that are conceptually more transparent, computationally less expensive, or converge faster. The new algorithms emerging from this study, namely, the modified m-D HARF and the m-D SHARF are compared with the earlier m-D HARF algorithm by explicitly deriving measures of computational complexities for both sequential and for parallel implementation, whenever appropriate. Performances of these new algorithms are also studied both theoretically and experimentally.