Wavelet frames have been successfully applied to various image restoration problems, such as denoising, inpainting, deblurring, etc. However, they are rarely used in geometric applications, except for recent work of [22, 23]. Motivated by the theoretical connection between wavelet frames based and total variation based image restoration models recently established in [8], we propose here a conv...

After the introduction of frame potentials by Benedetto and Fickus, there was an explosion of new results in frame theory. The generalization of this notation to weighted frame potentials yields a physical interpretation for finite frames along the lines of Coulomb’s law in physics. This allows us to use results from classical mechanics to anticipate new results in frame theory. All of this res...

Let L2(R,H) denote the space of all square integrable quaternionic-valued functions. In this article, let Φ∈L2(R,H). We consider perturbation problems wavelet frame {Φm,n,a0,b0,m,n∈Z} about translation parameter b0 and dilation a0. particular, we also research stability irregular {SmΦ(Smx−nb),m,n∈Z} for sampling.

Motivated by the notion of orthogonal frames, we describe sufficient conditions for the construction of orthogonal MRA wavelet frames in L(R) from a suitable scaling function. These constructions naturally lead to filter banks in `(Z) with similar orthogonality relations and, through these filter banks, the orthogonal wavelet frames give rise to a vector-valued discrete wavelet transform (VDWT)...

A systematic study on tight periodic wavelet frames and their approximation orders is conducted. We identify a necessary and sufficient condition, in terms of refinement masks, for applying the unitary extension principle for periodic functions to construct tight wavelet frames. Then a theory on the approximation orders of truncated tight frame series is established, which facilitates the const...