Some crystallographic Haar type composite dilation wavelets for P-4 = C-4 proportional to Z(2)

摘要

Composite dilation wavelets generate bases or frames using two groups of dilations. One group is associated with a set {a(i), a is an element of G(Ln) (R),i is an element of Z}, where a is an expanding matrix with det(a) an integer. The second group is associated with the subgroup B subset of SLn (R) of matrices b is an element of B with vertical bar det(b)vertical bar = 1. Here, we present crystallographic Haar type composite dilation wavelets generated by such two dilation groups associated with P-4 = C-4 proportional to Z(2). Further, we provide matricial filters and reconstruction formulae at various scales.