Non-convex compressed sensing CT reconstruction based on tensor discrete Fourier slice theorem

X-ray computed tomography (CT) scanners provide clinical value through high resolution and fast imaging. However, achievement of higher signal-to-noise ratios generally requires emission of more X-rays, resulting in greater dose delivered to the body of the patient. This is of concern, as higher dose leads to greater risk of cancer, particularly for those exposed at a younger age. Therefore, it is desirable to achieve comparable scan quality while limiting X-ray dose. One means to achieve this compound goal is the use of compressed sensing (CS). A novel framework is presented to combine CS theory with X-ray CT. According to the tensor discrete Fourier slice theorem, the 1-D DFT of discrete Radon transform data is exactly mapped on a Cartesian 2-D DFT grid. The nonuniform random density sampling of Fourier coefficients is made feasible by uniformly sampling projection angles at random. Application of the non-convex CS model further reduces the sufficient number of measurements by enhancing sparsity. The numerical results show that, with limited projection data, the non-convex CS model significantly improves reconstruction performance over the convex model.