论文标题
使用pr酸球波函数从球上傅立叶变换的数值重建
Numerical reconstruction from the Fourier transform on the ball using prolate spheroidal wave functions
论文作者
论文摘要
我们实现了[Isaev，Novikov，arxiv：2107.07882]的数值公式，以从$ \ Mathbb {r}^d $，$ d \ geq 1 $上找到紧凑的函数$ v $，从其傅立叶fromer transform $ \ mathcal $ \ mathcal {f} [f} [v] $中给出。对于一维情况，这些公式是基于pr酸球波函数的理论，尤其是在上述带限值的傅立叶变换的奇异值分解中，以$ d = 1 $。在多维中，这些公式还包括ra换的反转。特别是，我们给出了超分辨率的数值示例，即恢复超出衍射极限的细节。
We implement numerically formulas of [Isaev, Novikov, arXiv:2107.07882] for finding a compactly supported function $v$ on $\mathbb{R}^d$, $d\geq 1$, from its Fourier transform $\mathcal{F} [v]$ given within the ball $B_r$. For the one-dimensional case, these formulas are based on the theory of prolate spheroidal wave functions, which arise, in particular, in the singular value decomposition of the aforementioned band-limited Fourier transform for $d = 1$. In multidimensions, these formulas also include inversion of the Radon transform. In particular, we give numerical examples of super-resolution, that is, recovering details beyond the diffraction limit.
