Change Curve Estimation via Wavelets
提出用小波方法估计平面函数中的跳跃和尖点曲线，通过小波变换跨精细尺度实现，理论证明估计接近最优，模拟和真实图像验证了效果。
Abstract The recently developed theory of wavelets has a remarkable ability to “zoom in” on very short-lived frequency phenomena, such as transients in signals and singularities in functions, and hence provides an ideal tool to study localized changes. This article proposes a wavelet method for estimating jump and sharp cusp curves of a function in the plane. The method involves first computing wavelet transformation of data and then estimating jump and sharp cusp curves by wavelet transformation across fine scales. Asymptotic theory is established, and simulations are carried out to lend some credence to the asymptotic theory. The wavelet estimate is nearly optimal and can be computed by fast algorithms. The method is applied to a real image.