Numerous Applications of Wavelet Analysis
Leland Jameson, Toru Miyama, Takuji Waseda and Humio Mitsudera
International Pacific Reseach Center
Wavelet transforms provide information about a function or data set with respect to scale and location in contrast to Fourier transforms which provide a one parameter family of coeffircients representing the global frequency content. Wavelets are particularly useful for data analysis, image compression, numerical calculations and the list certainly does not end here.
In numerical computations, one often encounters computational data which has a variety of scales at different locations throughout the computation domain. Furthermore, the data can be dynamically moving throughout the computational domain. One might conjecture that such a computational environment could best be computed with a wavelet basis. However, numerical approaches where only a wavelet basis is used have serious flaws. Instead it is proposed that the Wavelet Optimized Finite Difference (WOFD) method be utilized. WOFD dyanamically moves with the data and focuses in on the data at the appropriate scale to resolve whatever scales are present. Furthermore, WOFD is 4th order in both space and time. This gives a far more accurate solution than, say, leapfrog or other low order methods which are commonly used in many computational fields.
In addition to introducing WOFD, we will also explore some other wavelet applications being pursued at the IPRC.
