Tomography of cylindrical objects: comparison of noise property and accuracy of Abel inversion techniques with and without noise filtering

Abstract

I have analyzed and compared the noise property and accuracy of three kinds of Abel inversion technique, i.e., the polynomial interpolation, versatile polynomial fitting (VPF) and modified Fourier-Hankel (MFH) methods. All these techniques will amplify noise due to the intrinsic property of Abel inversion. A technique that is more sensitive to noise also has a higher inversion accuracy for data without noise. Among the techniques without a noise resisting property, the third-degree polynomial interpolation and MFH methods have comparable performance and give higher inversion accuracies than other techniques. The VPF and MFH methods, which can be used without extra filtering of noise, yield markedly better results compared with those obtained by using noise filters in advance of inversion. Both of these two methods can be considered for applying to experimental data if there are no better smoothing techniques available.