论文标题
在球体上的多尺度最佳过滤
Multiscale Optimal Filtering on the Sphere
论文作者
论文摘要
我们提出了一个框架，以最佳滤波球形信号，并通过在球体上实现添加剂，零均值，不相关和各向异性噪声过程污染的球形信号。滤波是在球体上的尺度消失的小波变换给出的小波域中进行的。提出的过滤器是最佳的，因为它可以最大程度地减少过滤小波表示和无噪声信号的小波表示之间的均方误差。当使用方位对称小波函数时，我们还为过滤器提供了简化的滤波器公式。我们证明了在存在添加剂，零均值，不相关和白色高斯噪声的情况下，提出的最佳滤波器在地形图中的使用，并证明所提出的滤波器的性能要比硬阈值方法和加权球形谐波〜（加权 - pharm）信号估计框架更好。
We present a framework for the optimal filtering of spherical signals contaminated by realizations of an additive, zero-mean, uncorrelated and anisotropic noise process on the sphere. Filtering is performed in the wavelet domain given by the scale-discretized wavelet transform on the sphere. The proposed filter is optimal in the sense that it minimizes the mean square error between the filtered wavelet representation and wavelet representation of the noise-free signal. We also present a simplified formulation of the filter for the case when azimuthally symmetric wavelet functions are used. We demonstrate the use of the proposed optimal filter for denoising of an Earth topography map in the presence of additive, zero-mean, uncorrelated and white Gaussian noise, and show that the proposed filter performs better than the hard thresholding method and weighted spherical harmonic~(weighted-SPHARM) signal estimation framework.
