Let φ be a compactly supported symmetric real-valued refinable function in L2(R) with a finitely supported symmetric real-valued mask on Z. Under the assumption that the shifts of φ are stable, in this paper we prove that one can always construct three wavelet functions ψ, ψ and ψ such that (i) All the wavelet functions ψ, ψ and ψ are compactly supported, real-valued and finite linear combinati...

A tight wavelet frame is a natural generation of an orthonormal wavelet if redundancy is introduced into the wavelet system. By allowing redundancy, we gain the necessary flexibility to achieve such properties as symmetry and, more importantly, the short support and high vanishing moments of compactly supported wavelets. In addition, redundancy allows for the approximate shift invariance behavi...

A wavelet−based video coder built on the principles of distributed source coding is described. The encoder employs a syndrome−based encoding strategy for intercoded coefficients while other coefficients are intracoded using an embedded wavelet−based coder designed for the coding of arbitrarily shaped image objects. The decoder uses a reference frame in the domain of a redundant wavelet transfor...

We prove that any Parseval wavelet frame is the projection of an orthonormal wavelet basis for a representation of the Baumslag-Solitar group BS(1, 2) = 〈u, t | utu = t〉. We give a precise description of this representation in some special cases, and show that for wavelet sets, it is related to symbolic dynamics (Theorem 3.14). We show that the structure of the representation depends on the ana...

This paper outlines an adaptive wavelet-based perceptual audio coding scheme attending to various entropy-type criteria. Its performance using some different wavelet families and various filter lengths and decomposition depths has also been investigated. An optimal choice of these parameters is accomplished in order to evaluate both quality and bit rate of compressed signals for four different ...

In today’s streaming video content delivery infrastructure scalability is a highly desired feature. Not all the network enjoy the same bandwidth and as such the video servers should be able to provide different resolution and frame rate versions of the requested content without the need to re-encode the content to the desired bandwidth. Also video servers should be able to change the frame rate...

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...

In this paper, we investigate bit allocation strategies for a class of embedded wavelet video encoders. They take advantage of the precise control that such coders have over the bit-rate of each frame. We first show that a piecewise-linear model suits the rate distortion characteristics of these encoders better than an exponential model, specially in low bit-rate applications. Then, we use an e...

In today’s highly digitalized world maintaining the secrecy of the secret data is a vital problem. Steganography is an emerging area which may be used for secure transmission of the digital data. It is the art and science of embedding data into different covers such that the data embedded is imperceptible. The covers that can be used cover all forms of digital multimedia object namely text, ima...

The DFT based OFDM (DFT-OFDM) has currently drawn most of attention in the area of wireless communication. But, there is a long way to go to pursue higher bandwidth efficiency. Discrete wavelet transform has been proposed to substitute DFT, due to its higher spectral containment between subchannels, which can eliminate cyclic prefix (CP) that a must in DFT-OFDM system. In this paper, we propose...