Theory and application of two-dimensional nonseparable wavelet interpolation and approximation

In this dissertation, we present theory and applications of 2-D nonseparable wavelet interpolation and approximation. We give the necessary and sufficient conditions for a 2-D nonseparable scaling function and 2-D nonseparable multiscaling function possessing accuracy N. We show that their approximation can provide similar convergence properties as scalar wavelet system. In the numerical experiments, it appears that 2-D nonseparable scaling function interpolation has better convergence results than scalar wavelet systems in some cases. We also use 2-D nonseparable scaling function interpolation to perform image compression and image denoising. Experimental results show that there are some improvements and advantages of 2-D nonseparable scaling function interpolation.