Two-direction refinable functions and two-direction wavelets with high approximation order and regularity

作者：Yang Shou zhi^*; Li You fa

来源：Science in China Series A-Mathematics, 2007, 50(12): 1687-1704.

DOI：10.1007/s11425-007-0091-7

• two-direction refinable functions
• two-direction wavelets
• orthogonality
• approximation order
• regularity

where m >= 2 is an integer. Based on the positive mask {p(k)(+)} and negative mask {p(k)(-)}, the conditions that guarantee the above equation has compactly distributional solutions or L-2-stable solutions are established. Furthermore, the condition that the L-2-stable solution of the above equation can generate a two-direction MRA is given. The support interval of phi(x) is discussed amply. The definition of orthogonal two-direction refinable function and orthogonal two-direction wavelets is presented, and the orthogonality criteria for two-direction refinable functions are established. An algorithm for constructing orthogonal two-direction refinable functions and their two-direction wavelets is presented. Another construction algorithm for two-direction L-2-refinable functions, which have nonnegative symbol masks and possess high approximation order and regularity, is presented. Finally, two construction examples are given.

• 出版日期2007-12
• 单位汕头大学