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. © 2010 IEEE.

Nguyen H.T., Linh-Trung N.

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Từ khóa : Biorthogonal filters; De-noising; Design procedure; Filter designs; Framelets; Image de-noising; Laplacian Pyramid; Multi-rate processing; Numerical experiments; Perfect reconstruction; Scaling factors; Vanishing moment; Design; Filter banks; Information science; Laplace transforms; Signal processing; Noise pollution control