Alternative Derivations of M-Line Methods in Cone-Beam CT

摘要

In this work, we provide alternative derivations of backprojection-filtration (BPF) and filtered backprojection (FBP) reconstruction algorithms along M-lines in cone-beam CT. In the derivations of BPF algorithms, three different modified data functions are employed. One of the modified data functions is equivalent to the one in the original work except for a minus sign in our result. The other two modified data functions will result in an equivalent relationship without boundary terms compared to the original work. In our derivation of FBP algorithms along M-lines, we linked the object function to its Fourier data instead of its Radon data as in the original derivation. By doing so, we found that the BPF and FBP algorithms share exact same intermediate format. It turns out our derivation of FBP method along M-lines is a little simpler.