Lifting-based Laplacian Pyramid reconstruction schemes

Laplacian Pyramid (LP) provides a redundant signal representation and can be characterized as an oversampled filter bank (FB). In this paper, a generic lifting-based parameterization reconstruction algorithm is proposed to characterize all LP synthesis banks that can satisfy the perfect reconstruction property. Two typical lifting-based LP reconstruction schemes are then derived from this general representation. The first scheme presents the dual frame LP reconstruction and its closed-form solutions for any LP filters. The second LP reconstruction scheme leads to an efficient FB, which demonstrates improvements over the usual LP reconstruction in the presence of noise.