Application of a non-convex smooth hard threshold regularizer to sparse-view CT image reconstruction

In this work, we apply non-convex, sparsity exploiting regularization techniques to image reconstruction in computed tomography (CT). We modify the well-known total variation (TV) penalty to use a non-convex smooth hard threshold (SHT) penalty as opposed to the typical l(1) norm. The SHT penalty is different from the p < 1 norms in that it is bounded above and has bounded gradient as its argument approaches the zero vector. We propose a re-weighting scheme utilizing the Chambolle-Pock (CP) algorithm in an attempt to solve a data-error constrained optimization problem utilizing the SHT penalty and call the resulting algorithm SHTCP. We then demonstrate the algorithm on sparse-view reconstruction of a simulated breast phantom with noiseless and noisy data and compare the converged images to those generated by a CP algorithm solving the analogous data-error constrained problem utilizing the TV. We demonstrate that SHTCP allows for more accurate reconstruction in the case of sparse-view noisy data and, in the case of noiseless data, allows for accurate reconstruction from fewer views than its TV counterpart.