We study the problem of choosing an image based o p timal wavelet basis with compact support for image data compression and provide a general algorithm for computing the optimal wavelet basis. We parameterize the mother wavelet and scaling function of wavelet systems through a set of real coefficients of the relevant quadrature mirror filter (QMF) banks. We further introduce decomposition entro...

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 ...

In this paper a pair of wavelets are constructed on the basis of Hermite cubic splines. These wavelets are in C and supported on [−1, 1]. Moreover, one wavelet is symmetric, and the other is anti-symmetric. These spline wavelets are then adapted to the interval [0, 1]. The construction of boundary wavelets is remarkably simple. Furthermore, global stability of the wavelet basis is established. ...

In this paper a pair of wavelets are constructed on the basis of Hermite cubic splines. These wavelets are in C1 and supported on [−1, 1]. Moreover, one wavelet is symmetric, and the other is antisymmetric. These spline wavelets are then adapted to the interval [0, 1]. The construction of boundary wavelets is remarkably simple. Furthermore, global stability of the wavelet basis is established. ...

In image compression, the wavelet transformation is a state-of-the-art component. Recently, wavelet packet decomposition has received quite an interest. A popular approach for wavelet packet decomposition is the near-best-basis algorithm using nonadditive cost functions. In contrast to additive cost functions, the wavelet packet decomposition of the near-best-basis algorithm is only suboptimal....

A new method for measuring and designing smooth wavelet basis which dispenses with the need for having a large number of zero moments of the wavelet is given. The method is based on minimizing the “discrete finite variation”, and is a measure of the local “roughness” of a sampled version of the scaling function giving rise to “visually smooth” wavelet basis. Smooth wavelet basis are deemed to b...

0167-8655/$ see front matter 2010 Elsevier B.V. A doi:10.1016/j.patrec.2010.04.016 * Corresponding author. Tel.: +86 10 62788613x810 E-mail addresses: [email protected] edu.cn (W. Xu), [email protected] (Q. Dai). The most widely used basis selection algorithm for adaptive wavelet packets is the optimal basis selection method, which first grows a full wavelet packet tree and then...