Tomographic Reconstruction of Band-limited Hermite Expansions

In this work, we investigate the parallel-beam projection and reconstruction of band-limited Hermite expansions. Using a recently developed coordinate conversion technique, we show how the Fourier slice theorem can be directly applied. In our new approach, we do not introduce a non-integrable filter that appears in the filtered backprojection method. Since a projection of a 2D band-limited Hermite expansion is a 1D band-limited Hermite expansion and the coordinate conversion technique is lossless with this special expansion, we can avoid a series of approximations that the classical tomography techniques make.