In this paper, we first introduce the concept of an adaptive MRA (AMRA)
structure which is a variant of the classical MRA structure suited to the main
goal of a fast flexible decomposition strategy adapted to the data at each
decomposition level. We then study this novel methodology for the general case
of affine-like systems, and derive a Unitary Extension Principle (UEP) for
filter design. Finally, we apply our results to the directional representation
system of shearlets.