Cone-adapted continuous shearlet transform and reconstruction formula

The shearlet system generated by unitary representation of the shearlet group becomes unattractive due to biasedness towards one axis. Therefore, in this paper we study the cone-adapted shearlet system to cover whole R² and for giving equal treatment of all directions. Since the horizontal and vertical cones are treated similarly by just interchanging w 1 and w 2 , w = ( w 1 ; w 2 ) ∈ R² , we study only horizontal cone and derived some basic results concerning to continuous shearlet transform.