If the wavelet system {aψ(a ·−bk)}j,k∈Z forms a frame onL(R) for some a > 1 and b > 0, then it is called a (regular) wavelet frame. In this case we can reconstruct any f from the sampled values (Wψf)(a , abk). In practice the sampling points may be irregular. We need to know for which wavelet ψ and parameters {(sj , bk)}j,k , the wavelet system {s j ψ(sj · −bk)}j,k∈Z forms a frame on L (R). In ...

The algorithm of wavelet decomposition and reconstruction are applied in the audio error concealment method in this paper. When there is lost frame of the audio signal, the correct frames which lie before and after the lost frame are wavelet decomposed firstly. Then the two sets of the wavelet coefficients obtained from the wavelet decomposition are utilized to get the wavelet coefficients for ...

This article presents an analytic approach to study admissibility conditions related to classical full wavelet systems over finite fields using tools from computational harmonic analysis and theoretical linear algebra. It is shown that for a large class of non-zero window signals (wavelets), the generated classical full wavelet systems constitute a frame whose canonical dual are classical full ...

The aim of this paper is to study wavelet frame packets in which there are many frames. It is a generalization of wavelet packets. We derive few results on wavelet frame packets and have obtained the corresponding frame bounds.

this paper deals with continuous frames and continuous riesz bases. we introduce continuous riesz bases and give some equivalent conditions for a continuous frame to be a continuous riesz basis. it is certainly possible for a continuous frame to have only one dual. such a continuous frame is called a riesz-type frame [13]. we show that a continuous frame is riesz-type if and only if it is a con...

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...

In this paper, a new approach for echocardiography image compression is developed. To achieve a high rate of image compression as well as preserving the image information, motion detection and wavelet transform are combined. In the first step, a Region Of Interest (ROI) is determined and the image is divided into several (8 8 pixels) blocks. Thereafter, the motion vectors of each block are esti...