We introduce the concept of the modular function for a shiftinvariant subspace that can be represented by normalized tight frame generators for the shift-invariant subspace and prove that it is independent of the selections of the frame generators for the subspace. We shall apply it to study the connections between the dimension functions of wavelet frames for any expansive integer matrix A and...

Spacious experimental and numerical investigation has been conducted by researchers to increase the ductility and energy dissipation of concentrically braced frames. One of the most widely used strategies for increasing ductility and energy dissiption, is the use of energy-absorbing systems. In this regard, the cyclic behavior of a chevron bracing frame system equipped with multi-pipe dampers (...

Wavelet-based encoding is now emerging as an efficient way to encode video for streaming over the Internet and for wireless applications. Wavelet-based video coding has been recently added to the JPEG-2000 video standards. However, due to the lack of long wavelet encoded video streams, most research has so far been based on short video traces. This thesis paper presents a public library of trac...

Sparse approximation has shown to be a significant tool in improving image restoration quality, assuming that the targeted images can be approximately sparse under some transform operators. However, it is impossible for a fixed system to be always optimal for all the images. In this paper, we present an adaptive wavelet tight frame technology for sparse representation of an image with multiplic...

In this paper, we introduce a unified theory of tight wavelet frames on non-flat domains in both continuum setting, i.e. on manifolds, and discrete setting, i.e. on graphs; discuss how fast tight wavelet frame transforms can be computed and how they can be effectively used to process graph data. We start from defining multiresolution analysis (MRA) generated by a single generator on manifolds, ...

This paper devotes to analyzing deconvolution algorithms based on wavelet frame approaches, which has already appeared in [6,8,9] as wavelet frame based high resolution image reconstruction methods. We first give a complete formulation of deconvolution in terms of multiresolution analysis and its approximation, which completes the formulation given in [6,8,9]. This formulation converts deconvol...

There are intrinsic wavelet applications, by which we mean mathematical modeling of a physical phenomenon in which wavelet theory is the most natural quantitative means of explaining the phenomenon. This is not the same as the invaluable use of dyadic wavelets, say, as a tool with which to zoom-in or -out with regard to multi-scale phenomena. An example of an intrinsic wavelet application is wa...