论文标题
一种快速算法，用于反转亚伯的变换
A fast algorithm for the inversion of Abel's transform
论文作者
论文摘要
我们提出了一种用于计算逆Abel变换的新算法，该问题在许多物理和工程领域都出现。我们证明，给定函数的Legendre系数与与其亚abel变换相关的合适周期函数的傅立叶系数一致。这使我们能够通过单个快速傅立叶变换以简单，快速，准确的方式来计算逆亚伯变换的legendre系数。因此，该算法也适用于用代表嘈杂测量的样品给出的ABEL积分的反转。证明了严格的稳定性估计值，并通过一些数值实验也说明了算法的准确性。
We present a new algorithm for the computation of the inverse Abel transform, a problem which emerges in many areas of physics and engineering. We prove that the Legendre coefficients of a given function coincide with the Fourier coefficients of a suitable periodic function associated with its Abel transform. This allows us to compute the Legendre coefficients of the inverse Abel transform in an easy, fast and accurate way by means of a single Fast Fourier Transform. The algorithm is thus appropriate also for the inversion of Abel integrals given in terms of samples representing noisy measurements. Rigorous stability estimates are proved and the accuracy of the algorithm is illustrated also by some numerical experiments.
