We present a framework for the optimal filtering of spherical signals contaminated by realizations of zero-mean anisotropic noise processes. 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 uncorrelated, zero-mean, White Gaussian noise. The proposed filter is found to be superior to the hard thresholding method, particularly in the high noise regime.
翻译:我们提出了一个框架,用于最佳地过滤被零中性厌异噪音过程所污染的球状信号。过滤是在球体上分解波盘变换的波子域内进行的。提议的过滤是最佳的,因为它最大限度地减少了过滤过的波子表示和无噪音信号的波子表示之间的平均平方差。我们还为使用对称波子波子函数时的情况提供了一个简化的过滤器配方。我们展示了在不相关、零中度、白高斯噪音的情况下使用拟议的最佳过滤器对地球地形图进行分解。拟议的过滤器被认为优于硬阈值方法,特别是在高噪音系统中。