Wavelets are widely used in various disciplines to analyse signals both in space and scale. Whilst many fields measure data on manifolds (i.e., the sphere), often data are only observed on a partial region of the manifold. Wavelets are a typical approach to data of this form, but the wavelet coefficients that overlap with the boundary become contaminated and must be removed for accurate analysis. Another approach is to estimate the region of missing data and to use existing whole-manifold methods for analysis. However, both approaches introduce uncertainty into any analysis. Slepian wavelets enable one to work directly with only the data present, thus avoiding the problems discussed above. Applications of Slepian wavelets to areas of research measuring data on the partial sphere include gravitational/magnetic fields in geodesy, ground-based measurements in astronomy, measurements of whole-planet properties in planetary science, geomagnetism of the Earth, and cosmic microwave background analyses.

翻译：小波在各个领域中被广泛用于分析空间和尺度上的信号。虽然许多领域在流形上测量数据（即球体），但数据往往仅在流形的部分区域内被观察到。小波是处理这种数据的典型方法，但是与边界重叠的小波系数会受到污染，必须去除以进行准确分析。另一种方法是估计丢失数据的区域，并使用现有的全流形方法进行分析。然而，这两种方法都会导致任何分析中引入不确定性。Slepian小波可以直接处理仅现有数据，从而避免上述问题。在测量数据在部分球体上的研究领域中，应用Slepian小波的应用包括测地测量中的重力/磁场、天文地面测量、行星科学中的整体行星特性测量、地球的地磁学和宇宙微波背景分析。