In [1], Beylkin et al. introduced a wavelet-based algorithm that approximates integral or matrix operators of a certain type by highly sparse matrices, as the basis for efficient approximate calculations. The wavelets best suited for achieving the highest possible compression with this algorithm are Daubechies wavelets, while Coiflets lead to a faster decomposition algorithm at slightly lesser ...

With extensive digitization of data and increasing use of telemedicine, most of image data in hospitals are stored in digital form using picture archiving and communication systems. The need for data storage and bandwidth requirements is increasing and lossy compression techniques have become a necessity. The successful use of the wavelet transform in the field of image compression has been ext...

Biorthogonal wavelet-based full-approximation schemes are introduced in this paper for the numerical solution of elasto-hydrodynamic lubrication line and point contact problems. The proposed methods give higher accuracy in terms of better convergence with low computational time, which have been demonstrated through the illustrative problems.

In the past of two decades, wavelet methods have been adopted enthusiastically in many engineering applications such as signal and image processing. However, like most of the classic orthogonal expansions, wavelet expansions also exhibit Gibbs phenomenon around discontinuities of the original signals. Therefore, the recovered signals using wavelet expansions could be corrupted by the overshoot ...

An algebraic approach to the design of different binds of discrete wavelet transforma (orthogonal and biorthogonal single-/multiwavelet transforms, multiwavelet-like transforma) is taken. The different transfomrs are anaL ysed with respect to computational efforts, approzimation properties and symmetry. The design of the orthogonal and biorthogonal single-/multiwavelets requires the solution of...

In this paper, we analyze the design issues for the SPIHT (set partitioning in hierarchical trees) coding, one of the most prestigious embedded-wavelet-based algorithms in the literature. Equipped with the multiresolution decomposition, progressive scalar quantization and adaptive arithmetic coding, SPIHT generates highly compact scalable bitstreams suitable for real-time multimedia application...

Orthonormal bases of compactly supported wavelet bases correspond to subband coding schemes with exact reconstruction in which the analysis and synthesis filters coincide. We show here that under fairly general conditions, exact reconstruction schemes with synthesis filters different from the analysis filters give rise: to two dual Riesz bases of compactly supported wavelets. We give necessary ...

Digital image compression with multiresolution singular value decomposition is compared with discrete cosine transform, discrete 9/7 biorthogonal wavelet transform, Karhunen–Loève transform, and combinations thereof. The coding methods used SPIHT and run-length with Huffmann coding. The performances of these methods differ little from each other. Generally, the 9/7 biorthogonal wavelet transfor...

In both applications and wavelet theory, the spline wavelets are especially interesting, in part because of their simple structure. In a previous paper we proved that the function m;l is an m th order spline wavelet having an l th order spline dual wavelet. This enabled us to derive biorthogonal spline wavelet bases. In this paper we rst study the general structure of cardinal spline wavelets, ...

Over the last years, wavelet theory has been used with great success in a wide range of applications as signal denoising and image compression. An ideal image compression system must yield high-quality compressed image with high compression ratio. This paper attempts to find the most useful wavelet function to compress an image among the existing members of wavelet families. Our idea is that a ...