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：小波广泛应用于各个学科，用于在空间和尺度上分析信号。尽管许多领域在流形（如球面）上测量数据，但数据往往仅观测于该流形的局部区域。小波是处理此类数据的典型方法，但与小波系数重叠的边界区域会受到污染，必须去除才能实现精确分析。另一种方法是估计缺失数据区域，并使用现有的全流形方法进行分析。然而，这两种方法都会为任何分析引入不确定性。Slepian小波能够直接仅处理现有数据，从而规避上述问题。Slepian小波在测量局部球面数据的研究领域中的应用包括：大地测量学中的重力/磁场、天文学中的地面测量、行星科学中的行星整体特性测量、地球地磁学以及宇宙微波背景分析。