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.

中文翻译：

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球面上的多尺度最佳滤波

我们提出了一种对球形信号进行最佳滤波的框架，该球形信号被球体上的加性，零均值，不相关和各向异性噪声过程的实现所污染。在球上按比例尺离散的小波变换给出的小波域中执行滤波。从最小化滤波后的小波表示与无噪声信号的小波表示之间的均方误差的意义上说，所提出的滤波器是最佳的。当使用方位角对称小波函数时，我们还给出了滤波器的简化形式。我们演示了在存在加性，零均值，不相关和高斯白噪声的情况下，使用建议的最佳滤波器对地球地形图进行降噪的情况，