Slepian Scale-Discretised Wavelets on the Sphere

This work presents the construction of a novel spherical wavelet basis designed for incomplete datasets, i.e. datasets which are missing in particular region sphere. The eigenfunctions Slepian spatial-spectral concentration problem (the functions) set orthogonal functions more concentrated within defined region. allow one to compute convolution on sphere by leveraging recently proposed sifting and extending it any functions. Through tiling harmonic line, may construct scale-discretised wavelets. An illustration is presented based an example topographic map Earth. wavelets corresponding coefficients constructed from this used straightforward denoising example.