Recovering a compactly supported function from knowledge of its Hilbert transform on a finite interval

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.