Dept. of Diagnostic Radiol., Dartmouth-Hitchcock Med. Center, Lebanon, NH.
IEEE Trans Image Process. 1994;3(6):747-58. doi: 10.1109/83.336245.
Wavelet transforms are multiresolution decompositions that can be used to analyze signals and images. They describe a signal by the power at each scale and position. Edges can be located very effectively in the wavelet transform domain. A spatially selective noise filtration technique based on the direct spatial correlation of the wavelet transform at several adjacent scales is introduced. A high correlation is used to infer that there is a significant feature at the position that should be passed through the filter. The authors have tested the technique on simulated signals, phantom images, and real MR images. It is found that the technique can reduce noise contents in signals and images by more than 80% while maintaining at least 80% of the value of the gradient at most edges. The authors did not observe any Gibbs' ringing or significant resolution loss on the filtered images. Artifacts that arose from the filtration are very small and local. The noise filtration technique is quite robust. There are many possible extensions of the technique. The authors see its applications in spatially dependent noise filtration, edge detection and enhancement, image restoration, and motion artifact removal. They have compared the performance of the technique to that of the Weiner filter and found it to be superior.
小波变换是一种多分辨率分解，可以用于分析信号和图像。它们通过每个尺度和位置的功率来描述信号。在小波变换域中，可以非常有效地定位边缘。引入了一种基于几个相邻尺度上小波变换的直接空间相关性的空间选择性噪声滤波技术。高相关性用于推断在应该通过滤波器的位置存在显著特征。作者已经在模拟信号、幻影图像和真实的磁共振图像上测试了该技术。结果表明，该技术可以将信号和图像中的噪声含量降低 80%以上，同时保持大多数边缘处梯度值的至少 80%。作者在滤波后的图像上没有观察到任何吉布斯振铃或明显的分辨率损失。滤波产生的伪影非常小且局部。噪声滤波技术非常稳健。该技术有许多可能的扩展。作者认为它可以应用于空间相关的噪声滤波、边缘检测和增强、图像恢复和运动伪影去除。他们将该技术的性能与 Wiener 滤波器进行了比较，发现它具有优越性。
