In this paper, we characterize multiresolution analysis(MRA) Parseval frame multiwavelets in L^2(R^d) with matrix dilations of the form (D f )(x) = sqrt{2}f (Ax), where A is an arbitrary expanding dtimes d matrix with integer coefficients, such that |detA| =2. We study a class of generalized low pass matrix filters that allow us to define (and construct) the subclass of MRA tight frame multiwa...

We introduced the continuous and discrete $p$-adic shearlet systems. We restrict ourselves to a brief description of the $p$-adic theory and shearlets in real case. Using the group $G_p$ consist of all $p$-adic numbers that all of its elements have a square root, we defined the continuous $p$-adic shearlet system associated with $L^2left(Q_p^{2}right)$. The discrete $p$-adic shearlet frames for...

One of the major driven forces in the area of applied and computational harmonic analysis over the last decade or longer is the development of redundant systems that have sparse approximations of various classes of functions. Such redundant systems include framelet (tight wavelet frame), ridgelet, curvelet, shearlet and so on. This paper mainly focuses on a special class of such redundant syste...

We study spanning properties of a family functions translated along simple model sets. characterize tight frame and dual generators for such irregular translates we apply the results to Gabor systems. use connection between sets almost periodic rely strongly on Poisson summations formula introduce so-called bracket product, which then plays crucial role in our approach. As corollary main obtain...

Different from an orthonormal basis, a tight frame is an overcomplete and energy-preserving system with flexibility and redundancy. Many image restoration methods employing tight frames have been developed and studied in the literature. Tight wavelet frames have been proven to be useful in many applications. In this paper we are particularly interested in the image inpainting problem using dire...

In image restoration, we usually assume that the underlying image has a good sparse approximation under a certain system. Wavelet tight frame system has been proven to be such an efficient system to sparsely approximate piecewise smooth images. Thus it has been widely used in many practical image restoration problems. However, images from different scenarios are so diverse that no static wavele...