The Laplacian pyramid with rational scaling factors and application on image denoising

This paper considers the Laplacian pyramid (LP) with rational scaling factors. Desired properties, namely perfect reconstruction, vanishing moment, and smoothness of framelets, and their corresponding mathematical conditions for the filters are discussed. A design procedure to obtain near biorthogonal filters for the rational LP is then proposed. Numerical experiments demonstrate the advantages of the rational LP over the traditional dyadic LP on denoising application.