Level Set Reconstruction for Sparse Angularly Sampled Data

We propose an iterative tomographic reconstruction algorithm from sparse angularly sampled projections for applications where the underlying data is well approximated as a piecewise constant function. We impose this a priori constraint of the underlying data by using the multiphase level set framework introduced by Vese et al. As a result, level set method is incorporated into the updates of the proposed iterative reconstruction algorithm. Using our proposed algorithm, we reconstruct from 13 projections of a numerical chest phantom uniformly sampled over 180deg and compare it with reconstructions by unfiltered backprojection, filtered backprojection, and maximum likelihood expectation maximization (MLEM) algorithm. Results show that there is no loss of reconstruction quality for the noise-free case and improved image quality for the noisy case. Our results are promising for a broad spectrum of applications where the number of projections are inherently limited.