SINGULARITY DETECTION AND PROCESSING WITH WAVELETS
SINGULARITY DETECTION AND PROCESSING WITH WAVELETS
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DOI：
10.1109/18.119727
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发表时间：
1992-03-01
影响因子：
2.5
通讯作者：
HWANG, WL
中科院分区：
文献类型：
--
作者：
MALLAT, S;HWANG, WL
大多数信号信息通常是由不规则结构和瞬时现象传递的。用Lipschitz指数对奇异性的数学表征进行了解释。回顾了定理，该定理估算了跨小波变换尺度的进化中局部Lipschitz指数。然后证明，小波的局部最大值转换模量检测到不规则结构的位置，并提供了计算其Lipschitz指数的数值程序。具有快速振荡的奇点的小波变换具有分别研究的特定行为。这种振荡的局部频率是从小波变换模量最大值测量的。从数值上证明，可以从其小波变换模量的局部最大值中重建一维信号，并具有良好的近似值。作为应用程序，开发了一种算法，该算法通过分析跨尺度的小波变化最大值的演变来消除信号中的白色噪声。在二维中，小波变换最大值表示边缘在图像中的位置。将授予算法扩展以增强图像。
Most of a signal information is often carried by irregular structures and transient phenomena. The mathematical characterization of singularities with Lipschitz exponents is explained. Theorems are reviewed that estimate local Lipschitz exponents of functions from the evolution across scales of their wavelet transform. It is then proven that the local maxima of the wavelet transform modulus detect the locations of irregular structures and provide numerical procedures to compute their Lipschitz exponents. The wavelet transform of singularities with fast oscillations have a particular behavior that is studied separately. The local frequency of such oscillations are measured from the wavelet transform modulus maxima. It has been shown numerically that one- and two-dimensional signals can be reconstructed, with a good approximation, from the local maxima of their wavelet transform modulus. As an application, an algorithm is developed that removes white noises from signals by analyzing the evolution of the wavelet transform maxima across scales. In two-dimensions, the wavelet transform maxima indicate the location of edges in images. The denoising algorithm is extended for image enhancement.