It has been well established that critically sampled boundary pre-/postfiltering operators can improve the coding efficiency and mitigate blocking artifacts in traditional discrete cosine transform-based block coders at low bit rates. In these systems, both the prefilter and the postfilter are square matrices. This paper proposes to use undersampled boundary pre- and postfiltering modules, where the pre-/postfilters are rectangular matrices. Specifically, the prefilter is a "fat" matrix, while the postfilter is a "tall" one. In this way, the size of the prefiltered image is smaller than that of the original input image, which leads to improved compression performance and reduced computational complexities at low bit rates. The design and VLSI-friendly implementation of the undersampled pre-/postfilters are derived. Their relations to lapped transforms and filter banks are also presented. Two design examples are also included to demonstrate the validity of the theory. Furthermore, image coding results indicate that the proposed undersampled pre-/postfiltering systems yield excellent and stable performance in low bit-rate image coding.
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