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近年来子波变换已为越来越多的人熟,尽管应用子波变换的概念已有相当一段时间,但是,只是到最近几年才开始产生作用,尤其是在信号和图象处理方面。子波概念可以应用在差方方程、信号处理、图象和视频压缩以及许多其它领域。我们将对子波变换和子波分析作一简要介绍,并将子波变换同傅里叶变换作一比较。子波变换使我们能够分析非静态信号,而傅里叶变换却不能,这是子波的一个十分重要的特征。子波分解使得同时在时域(空域)和频域分析一个信号成为可能,适合于多分辨率分析。子波最今人感兴趣的一项应用就是图象复合。对于这一应用,我们可取来自不同敏感器(例如,可见光和红外)的图象的子波变换。这给我们提供了可见光和红外图象的多分辨率描述。然后两种图象在每个分辨率水平上汇合。运用对所形成图象的逆向子波变换,产生一幅新的图象,该图象就是两幅原始图象的复合图。这一原理可以应用到两幅以上的图象上,无论这些图象是否在同一光谱波段内。本文将给出一些结果,并与Burt和Toet的经典棱锥算法进行比较。
Wavelet transformation has become more and more popular in recent years. Although the concept of wavelet transformation has been used for quite some time, it has only begun to play an active role in recent years, especially in signal and image processing. Wavelet concepts can be applied to the equation of the difference, signal processing, image and video compression, and many others. We will make a brief introduction of wavelet transform and wavelet analysis, and compare the wavelet transform with the Fourier transform. Wavelet transform allows us to analyze non-static signals, but not Fourier transform, which is a very important feature of wavelet. Wavelet decomposition makes it possible to analyze a signal simultaneously in the time domain (airspace) and the frequency domain, making it suitable for multiresolution analysis. One of the most interesting applications of wavelet is image composition. For this application we prefer wavelet transforms from images of different sensors (eg visible and infrared). This gives us a multi-resolution description of visible and infrared images. The two images are then merged at each resolution level. Using the inverse wavelet transform of the resulting image, a new image is generated, which is a composite of the two original images. This principle can be applied to more than two images, whether the images are in the same spectral band or not. This article will give some results and compare them with Butr and Toet’s classic pyramid algorithm.