Multivariate multiresolution with multiwavelets

In this thesis, we will study function approximation with wavelets. Using a wavelet basis allows us to represent a function in L^2(R^n) at various levels of resolution. In other words, we have a multiresolution representation of a square integrable, multivariate function. We study smoothing, denoising, and compression of a function using multiresolution analysis. The choice of dierent wavelet bases and one multiwavelet basis are explored. Both regular and irregular sampling cases are studied. Our conclusion that multivariate multiresolution is better with wavelets than with multiwavelets is due to the difficulty of selecting the correct prelter for function approximations with multiwavelets.