Toward recursive spherical harmonics-issued bi-filters: Part I: theoretical framework

This work lies in the whole topic of signal/image processing based on frequency decompositions. These are indeed applied in a variety of subjects such as estimation, reconstruction, shape recognition, filtering $$\dots $$⋯. Among these decompositions, spherical harmonics are widely used. Mathematically, spherical harmonics are special functions obtained as particular solutions of the Laplace equation generated by Legendre polynomials. Using the three-level recurrence relation of these polynomials, spherical harmonics recursive bases are revisited allowing the decompositions of signals in eigenmodes similar to Fourier ones. Special filters have been constructed and proved to be more efficient and accurate than existing ones as they lead to faster and more accurate algorithms.

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