meyer小波变换像空间再生核函数word论文.docxVIP

Meyer 小波变换像空间的再生核函数摘要小波分析是是纯粹数学与应用数学及工程技术殊途同归的光辉典范，给许 多相关领域提供了强有力的工具。众所周知，连续小波变换是小波分析的基础。 连续小波变换的像空间是一个再生核Hilbert空间，而再生核Hilbert空间中的元 素都能由该空间的再生核函数表示。可见，再生核Hilbert空间是连续小波变换 的基础，没有再生核函数，连续小波变换就无法进行重建，更谈不上小波分析 方法。因此研究连续小波变换的像空间的再生核函数是描述该像空间性质的首 要任务。本文针对Meyer小波和单周正弦小波展开讨论。Meyer小波是一类经典小波，它具有无限次可微、衰减速度快、光滑性和 频谱有限等良好性质。在信号的检测、图像处理等方面被广泛应用。本文通过 选定适当的光滑函数得到一个具体的Meyer小波。针对这个Meyer小波，首先， 讨论了Meyer小波是可允许小波，并给出Meyer小波变换估计式和等距恒等式。 其次，给出了Meyer小波变换像空间再生核函数的具体表达式，并证明了这个再生核函数是连续函数，而且当固定尺度因子时，对Meyer小波变换像空间的 再生核函数做了进一步刻画。最后，给出Meyer小波变换像空间的采样定理。 单周正弦小波是具有紧支撑区间的小波，虽然它不是一个可允许小波，但 是具有无限次可微性，所以单周正弦波是一个光滑程度较好的小波函数，在信 号处理方面得到较好的应用。文中给出了单周正弦小波变换像空间的再生核函数的具体表达式。关键词 再生核；采样定理；Meyer 小波；正弦波The Reproducing Kernel of Meyer Wavelet Transform Image SpaceAbstractWavelet analysis is a shining example of which converge the pure mathematics, applied mathematics and engineering together, at the same time, it provide a powerful tool for many fields. We all know that the continuous wavelet transform is the basis of wavelet analysis. The image space of continuous wavelet transform is a reproducing kernel Hilbert space. The elements of the reproducing kernel Hilbert space are expressed by its reproducing kernel function, Because Reproducing Kernel Hilbert space is the basis of continuous wavelet transform, without reproducing kernel function, continuous wavelet transform can not be rebuilt. and not to exist the wavelet analysis. Therefore, to research reproducing kernel function is very important basic work before describing the reproducing kernel space. In this paper, we will discussion the single week sine wavelet and Meyer wavelet.Meyer wavelet is a classic wavelet, it has many good properties. For example derivation infinitely, smoothness, attenuates fast and its spectrum is finite, it is widely used in signal detection, image processing, etc. In this paper, we get a specific Meyer wavelet by selecting the appropriate smooth function. For the Meyer wavelet, Firstly, geting the Meyer wavelet is permissible wav