Wavelet Families of Increasing Order in Arbitrary Dimensions

Wavelet Families of Increasing Order
in Arbitrary Dimensions

Jelena Kovacevic Wim Sweldens

Abstract: We build compactly supported biorthogonal wavelets and perfect reconstruction filter banks for any lattice in any dimension with any number of primal and dual vanishing moments. The resulting scaling functions are interpolating. Our construction relies on the lifting scheme and inherits all of its advantages: fast transform, in-place calculation, and integer-to-integer transforms. We show that two lifting steps suffice: predict and update. The predict step can be built using multivariate polynomial interpolation, while update is a multiple of the adjoint of predict.

Status: IEEE Trans. Image Proc., vol. 9, nr. 3, pp. 480-496, 2000.

Dates:

May 1999:

Revised posting. An earlier mistake in the FCO and checkboard lattice section pointed out by Jeremy McDonald has been corrected.
December 1997:

Initial posting.

Download: PDF v3.0 (.pdf) (392K).

BiBTeX entry:


   @article{ks:mdlift,
    author = {J. Kova\v{c}evi\'{c} and W. Sweldens},
    title = {Wavelet Families of Increasing Order in Arbitrary Dimensions},
    journal = {IEEE Trans. Image Proc.},
    month = {March},
    volume = 9,
    number = 3,
    pages = {480-496},
    year = {2000}		  
   }