Accurate image reconstruction from few-view and limited-angle data in diffraction tomography.

We present a method for obtaining accurate image reconstruction from highly sparse data in diffraction tomography (DT). A practical need exists for reconstruction from few-view and limited-angle data, as this can greatly reduce required scan times in DT. Our method does this by minimizing the total variation (TV) of the estimated image, subject to the constraint that the Fourier transform of the estimated image matches the measured Fourier data samples. Using simulation studies, we show that the TV-minimization algorithm allows accurate reconstruction in a variety of few-view and limited-angle situations in DT. Accurate image reconstruction is obtained from far fewer data samples than are required by common algorithms such as the filtered-backpropagation algorithm. Overall our results indicate that the TV-minimization algorithm can be successfully applied to DT image reconstruction under a variety of scan configurations and data conditions of practical significance.