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目的：当前，以原子力显微镜为代表的扫描探针显微镜设备可以获取纳米尺度薄膜样品的表面图像，但这些图像存在不同程度的噪声，影响图像质量和信息判断。为了更准确获取这些薄膜表面状态，需要对薄膜样品表面图像数据和信息进行降噪处理。方法结合AFM等设备成像特点以及小波变换的时频局域性特点，在介绍小波变换基本理论和噪声来源分析基础上，提出了一种多层小波分解去噪算法。传统的信号理论是建立在傅里叶变换基础上的，而傅里叶变换作为一种全局性的变化，其有一定的局限性，无法同时表述信号在时域和频域的局部性质，而这些局部特征恰恰是非平稳信号性质最关键的部分。小波变换保留了窗口傅里叶变换局部化的优点，改变了窗口傅里叶变换窗口函数大小固定的缺点。结果原始图像信号的频率在0 Hz到4000 Hz都有分布。通过小波变换后，信号波形更光滑，频谱在500 Hz到2000 Hz之间分布。结论将小波变换应用于薄膜表面图像信号降噪中，通过实验证明通过小波变换可以有效去除信号中的噪声部分。

ABSTRACT:Objective The surface images of nano-scale thin film samples can be obtained by the scanning probe micro-scope device represented by atomic force microscope, but these images have different degrees of noise, which affect the quality of the image and the judgment of image information. In order to obtain the surface state of the film more accurately, noise re-duction of the surface image data and information of the sample is needed.Methods This paper proposed a multi-layer wavelet decomposition noise reduction algorithm based on the introduction of the basic theory of wavelet transform and the analysis of noise sources by combining the imaging characteristics of equipment such as AFM and the time-frequency locality characteris-tics of wavelet transform. Fourier transform is the basis of the traditional theory of signal, but it has some limitations as a kind of global change. Fourier transform fails to simultaneously describe the local characteristics of the time domain and the frequency domain, which are the key parts of unstable signal characteristics. The wavelet transform kept the advantage of window Fourier transforms in localization and changed its defect of fixed size.Results The frequency of the original image signal was distri-buted in the range of 0~4000 Hz. After the wavelet transform, the signal waveform was more smooth, and the frequency spec-trum was distributed between 500 Hz and 2000 Hz.Conclusion The wavelet transform was applied to signal noise reduction of the film surface images, and the experiment proved that the noise could be effectively removed using wavelet transform.