论文标题
对球体的功能惩罚基础追求
Functional Penalised Basis Pursuit on Spheres
论文作者
论文摘要
在本文中，我们提出了一个统一的理论和实用的球形近似框架，用于高超氧化物的功能逆问题。更具体地说，我们考虑使用具有GTV正则化项的功能惩罚基础问题问题直接在连续域中恢复球场。我们的框架与各种测量类型以及非不同的凸成本功能兼容。通过一个新颖的代表定理，我们用稀疏创新的球形花样来表征他们的解决方案集。我们使用此结果来得出近似规范的基于样条的离散方案，并消失了近似误差。为了解决所得的有限维优化问题，我们提出了一种有效的且可收敛的原始偶发分裂算法。我们在环境科学领域的真实示例中说明了框架的多功能性。
In this paper, 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.
