Date of Award
Doctor of Philosophy
We review the one-dimensional setting of wavelet theory and generalize it to nonseparable multivariate wavelets. This process presents significant technical difficulties. Some techniques of the one-dimensional setting carry over in a more or less straightforward way; some do not generalize at all.;The main results include the following: an algorithm for computing the moments for multivariate multiwavelets; a necessary and sufficient condition for the approximation order; the lifting scheme for multivariate wavelets; and a generalization of the method of Lai  for the biorthogonal completion of a polyphase matrix under suitable conditions.;One-dimensional techniques which cannot be generalized include the factorization of the polyphase matrix, and a general solution to the completion problem.
Digital Repository @ Iowa State University, http://lib.dr.iastate.edu
Ghan Shyam Bhatt
Bhatt, Ghan Shyam, "Nonseparable multivariate wavelets " (2004). Retrospective Theses and Dissertations. 1145.