Implementation of new biorthogonal filter banks (BFB) for image compression and denoising is performed, using test images with diversified characteristics. These new BFB’s are linear-phase, have odd lengths, and with a critical feature, namely, the filters preserve signal energy very well. Experimental results show that the proposed filter banks demonstrate promising performance improvement over the filter banks of those widely used in the image processing area, such as the CDF 9/7.

In a recent work, Selesnick constructed two GHM-like scaling function vectors of dimension two that allow balanced multiwavelet decomposition. In this letter, we construct such multiwavelets and give the corresponding decomposition/reconstruction filters. Symmetry and/or antisymmetry are achieved and filterbank shifts are investigated. The fundamental tools for the study of this problem area are presented in the second and third sections for completeness.

The notion of armlets is introduced in this letter as a precise formulation of orthonormal multiwavelets that guarantee wavelet decomposition with highpass output not being effected by polynomial perturbation of the input. A mathematical scheme for constructing armlets is given, and it is shown that the notions of armlets and balanced multiwavelets are different. In particular, while balanced wavelets are armlets, the converse is false in general. One advantage of armlets is that the weaker assumption provides flexibility to facilitate wavelet and filter construction.