Four-Point Wavelets and Their Applications

Multiresolution analysis (MRA) and wavelets provide useful andefficient tools for representing functions at multiple levels ofdetails. Wavelet representations have been used in a broad rangeof applications, including image compression, physical simulationand numerical analysis.In this paper, the authors construct a new class of wavelets,called four-point wavelets, based on an interpolatory four-pointsubdivision scheme. They are of local support, symmetric andstable. The analysis and synthesis algorithms have linear timecomplexity. Depending on different weight parameters w, thescaling functions and wavelets generated by the four-point subdivisionscheme are of different degrees of smoothness. Therefore the user canselect better wavelets relevant to the practice among the classes ofwavelets. The authors apply the four-point wavelets in signal compression.The results show that the four-point wavelets behave much betterthan B-spline wavelets in many situations.