Iterated oversampled filter banks and wavelet frames

This paper takes up the design of wavelet tight frames that are analogous to Daubechies orthonormal wavelets - that is, the design of minimal length wavelet filters satisfying certain polynomial properties, but now in the oversampled case. The oversampled dyadic DWT considered in this paper is based on a single scaling function and two distinct wavelets. Having more wavelets than necessary gives a closer spacing between adjacent wavelets within the same scale. As a result, the transform (like Kingsbury's dual-tree DWT) is nearly shift-invariant, and can be used to improve denoising. Because the associated time-frequency lattice preserves the dyadic structure of the critically sampled DWT (which the undecimated DWT does not) it can be used with tree-based denoising algorithms that exploit parent-child correlation.