Iterative total-variation reconstruction versus weighted filtered-backprojection reconstruction with edge-preserving filtering

Iterative image reconstruction with the total-variation (TV) constraint has become an active research area in recent years, especially in x-ray CT and MRI. Based on Green's one-step-late algorithm, this paper develops a transmission noise weighted iterative algorithm with a TV prior. This paper compares the reconstructions from this iterative TV algorithm with reconstructions from our previously developed non-iterative reconstruction method that consists of a noise-weighted filtered backprojection (FBP) reconstruction algorithm and a nonlinear edge-preserving post filtering algorithm. This paper gives a mathematical proof that the noise-weighted FBP provides an optimal solution. The results from both methods are compared using clinical data and computer simulation data. The two methods give comparable image quality, while the non-iterative method has the advantage of requiring much shorter computation times. (paper)