The iterative next-neighbor regridding (INNG) algorithm combined with TV regularization used for reconstruction in diffraction tomography

In diffraction tomography, gridding is often required to interpolate the non-Cartesian sampled data into a Cartesian coordinate. In this paper, the iterative next-neighbor regridding (INNG) algorithm is used to meet the need. Nevertheless, as well as in other gridding algorithms, interpolating non-Cartesian data to a Cartesian grid introduces errors, resulting in artifacts. Considering that total variation (TV) regularization can remove small oscillations by noise and Gibbs phenomenon while preserving edges, we combine the INNG algorithm with TV regularization to reconstruct images in diffraction tomography. The hybrid method was compared with the original INNG algorithm and NUFFT based on TV regularization. Computer simulation results demonstrate that it largely improves reconstruction quality to the INNG algorithm and obtains lower root mean square error (RMSE) than the other two methods.