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For compactly supported symmetric-antisymmetric orthonormal multiwavelet systems with multiplicity 2, we first show that any length-2N multiwavelet system can be constructed from a length-(2N + 1) multiwavelet system and vice versa. Then we present two explicit formulations for the construction of multiwavelet functions directly from their associated multiscaling functions. This is followed by the relationship between these multiscaling functions and the scaling functions of related orthonormal scalar wavelets. Finally, we present two methods for constructing families of symmetric-antisymmetric orthonormal multiwavelet systems via the construction of the related scalar wavelets.

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The widespread use of block-based interframe motion estimation for video sequence compression in both MPEG and H.263 standards is due to its effectiveness and simplicity of implementation. Nevertheless, the high computational complexity of the full-search algorithm has motivated a host of suboptimal but faster search strategies. A popular example is the three-step search (TSS) algorithm. However, its uniformly spaced search pattern is not well matched to most real-world video sequences in which the motion vector distribution is nonuniformly biased toward the zero vector. Such an observation inspired the new three-step search (NTSS) which has a center-biased search pattern and supports a halfway-stop technique. It is faster on the average, and gives better motion estimation as compared to the well-known TSS. Later, the four-step search (4SS) algorithm was introduced to reduce the average case from 21 to 19 search points, while maintaining a performance similar to NTSS in terms of motion compensation errors. In this paper, we propose a novel unrestricted center-biased diamond search (UCBDS) algorithm which is more efficient, effective, and robust than the previous techniques. It has a best case scenario of only 13 search points and an average of 15.5 block matches. This makes UCBDS consistently faster than the other suboptimal block-matching techniques. This paper also compares the above methods in which both the processing speed and the accuracy of motion compensation are tested over a wide range of test video sequences.