Some crystallographic Haar type composite dilation wavelets for P4 = C4 ⋉ ℤ2

Composite dilation wavelets generate bases or frames using two groups of dilations. One group is associated with a set [Formula: see text] where [Formula: see text] is an expanding matrix with [Formula: see text] an integer. The second group is associated with the subgroup [Formula: see text] of matrices [Formula: see text] with [Formula: see text] Here, we present crystallographic Haar type composite dilation wavelets generated by such two dilation groups associated with [Formula: see text] Further, we provide matricial filters and reconstruction formulae at various scales.