Recovering a compactly supported function from knowledge of its Hilbert transform on a finite interval
Recovering a compactly supported function from knowledge of its Hilbert transform on a finite interval
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DOI：
10.1109/lsp.2004.840899
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发表时间：
2005-02-01
影响因子：
3.9
通讯作者：
Pan, X
中科院分区：
文献类型：
--
作者：
Sidky, EY;Pan, X
在层析成像和信号处理的某些算法中，有限希尔伯特变换的求逆是一个关键步骤。本文提出了一种求有限希尔伯特变换的新方法，该方法只需要有限区间上的数据。将该方法与求解翼型积分方程组的雅可比多项式配置法进行了比较，该方法等价于有限希尔伯特变换的逆变换。定量结果表明，与配置法和其他方法相比，新方法具有更高的精度和更少的数据噪声影响。
Inverting the finite Hilbert transform is a crucial step in some algorithms for tomographic imaging and signal processing. In this letter, a new method for inverting the finite Hilbert transform that requires data only on a finite interval is proposed. The new method is compared to the Jacobi-polynomial collocation method, which is employed for solving the airfoil integral equation, which is equivalent to inverting the finite Hilbert transform. Quantitative results show that the new method is more accurate and less susceptible to data noise than collocation and other methods.