Functional Penalised Basis Pursuit on Spheres

In this work, we propose a unified theoretical and practical spherical approximation framework for functional inverse problems on the hypersphere. More specifically, we consider recovering spherical fields directly in the continuous domain using functional penalised basis pursuit problems with gTV regularisation terms. Our framework is compatible with various measurement types as well as non-differentiable convex cost functionals. Via a novel representer theorem, we characterise their solution sets in terms of spherical splines with sparse innovations. We use this result to derive an approximate canonical spline-based discretisation scheme, with vanishing approximation error. To solve the resulting finite-dimensional optimisation problem, we propose an efficient and provably convergent primal-dual splitting algorithm. We illustrate the versatility of our framework on real-life examples from the field of environmental sciences.


Published in:
Applied and Computational Harmonic Analysis
Year:
2020
Note:
Supplementary material: https://matthieumeo.github.io/
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Note: The status of this file is: Anyone


 Record created 2020-06-11, last modified 2020-06-15

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