球谐展开的稀疏恢复

球谐熵用于最优3D建模

Spherical harmonics entropy for optimal 3D modeling

本文提出基于球谐分析的图像重建方法，利用球谐熵评估重建图像的有序性，通过模拟研究验证了方法的效率和准确性。

球面拓扑曲面平均曲率流的球谐伪谱方法

A spherical harmonic pseudo-spectral approach to mean curvature flow of surfaces with spherical topology

提出一种球谐伪谱方法求解球面拓扑闭曲面的平均曲率流，通过球谐函数离散化Dziuk方法的弱形式，证明位置误差的指数收敛性，数值实验验证理论结果。

FaVeST: Fast Vector Spherical Harmonic Transforms

Vector spherical harmonics on the unit sphere of $\mathbb{R}^3$ have broad applications in geophysics, quantum mechanics and astrophysics. In the representation of a tangent vector field, one needs to evaluate the expansion and the Fourier coefficients of vector spherical harmonics. In this paper, we develop fast algorithms (FaVeST) for vector spherical harmonic transforms on these evaluations. The forward FaVeST evaluates the Fourier coefficients and has a computational cost proportional to $N\log \sqrt{N}$ for $N$ number of evaluation points. The adjoint FaVeST which evaluates a linear combi…

Near Optimal Reconstruction of Spherical Harmonic Expansions

We propose an algorithm for robust recovery of the spherical harmonic expansion of functions defined on the d-dimensional unit sphere $\mathbb{S}^{d-1}$ using a near-optimal number of function evaluations. We show that for any $f \in L^2(\mathbb{S}^{d-1})$, the number of evaluations of $f$ needed to recover its degree-$q$ spherical harmonic expansion equals the dimension of the space of spherical harmonics of degree at most $q$ up to a logarithmic factor. Moreover, we develop a simple yet efficient algorithm to recover degree-$q$ expansion of $f$ by only evaluating the function on uniformly sa…

球谐展开的快速算法，III

Fast algorithms for spherical harmonic expansions, III

利用蝴蝶方案加速球谐变换计算，通过深度优先遍历控制流图组织预计算，为多级过程提供高效替代方法。

关于球谐函数离散化中的最大值原理

On a maximum principle in discretization with spherical harmonics

本文针对球谐函数离散化中拉普拉斯方程的离散解不满足最大值原理的问题，推导了使离散解满足最大值原理的r_N^max的精确估计，并分析了估计的尖锐性。