正交小波展开的Gibbs现象(英文)

Gibbs Phenomenon in Orthogonal Wavelet Expansion

近十年来 ,随着小波理论和应用的迅猛发展 ,对于小波的 Gibbs现象也吸引了来自不同领域的研究兴趣 .这是因为在某些应用领域中 ,特别是在信号处理和图像处理的应用中 ,这一现象影响了预期的效果 .研究者们为减弱和消除这一现象付出了许多努力 .这篇文章主要讨论和总结了在小波的离散正交展开中的 Gibbs现象 .文章强调了 summability方法的最近发展并对于其他方法和结果列出了参考文献 .文章在最后讨论了正在研究中的一些有待于解决的相关问题 .

With the wavelet theory and its applications being developed explosively in the last decade or so, the research on Gibbs phenomenon in the context of wavelet approximation has attracted interests of some researchers and practitioners from different areas. Many efforts have been made to eliminate or remove this behavior when it is unwanted in some applications, such as in signal and image processing. In this article, our attention is given to the Gibbs phenomenon in the discrete orthogonal wavelet expansion. We highlight the summability methods developed lately and refer to the literature for a variety of techniques and results. We also post some open problems which are under our investigation.