When
Where
Speaker: Noah McCollum-Gahley, Applied Mathematics
Title: Mathematical and computational framework behind the inverse Radon transform and tomographic reconstruction
Abstract: Tomographic imaging relies on recovering an unknown function from its line integrals, a problem classically solved by the inverse Radon transform. In this talk, I outline a from-scratch implementation of filtered back-projection, a foundational algorithm underlying computed tomography. Beginning with the Radon transform and its Fourier relationship via the Fourier Slice Theorem, I show how projections taken at multiple angles can be assembled into the two-dimensional Fourier spectrum of the original image by taking "slices" of the one dimensional Fourier transform. I then discuss the computational realization of this process, including discretization, interpolation of off-grid frequency samples, and efficient reconstruction through the inverse FFT. I conclude the presentation with reconstruction results and discussion of sources of error.