Combined Energy Minimization for Image Reconstruction from Few Views

Reconstruction from few views is an important problem in medical imaging and applied mathematics. In this paper, a combined energy minimization is proposed for image reconstruction. l 2 energy of the image gradient is introduced in the lower density region, and it can accelerate the reconstruction speed and improve the results. Total variation of the image is introduced in the higher density region, and the image features can be preserved well. Nonlinear conjugate gradient method is introduced to solve the problem. The efficiency and accuracy of our method are shown in several numerical experiments.