Model-based X-ray CT image and light field reconstruction using variable splitting method

Model-based iterative reconstruction (MBIR) is a powerful technique for solving ill-posed inverse problems. Compared with direct methods, it can provide better estimates from noisy measurements and from incomplete data, at the cost of much longer computation time. In this work, we focus on accelerating and applying MBIR for solving reconstruction problems, including X-ray computed tomography (CT) image reconstruction and light field reconstruction, using variable splitting based on the augmented Lagrangian (AL) methods. For X-ray CT image reconstruction, we combine the AL method and ordered subsets (OS), a well-known technique in the medical imaging literature for accelerating tomographic reconstruction, by considering a linearized variant of the AL method and propose a fast splitting-based ordered-subset algorithm, OS-LALM, for solving X-ray CT image reconstruction problems with penalized weighted least-squares (PWLS) criterion. Experimental results show that the proposed algorithm significantly accelerates the convergence of X-ray CT image reconstruction with negligible overhead and greatly reduces the noise-like OS artifacts in the reconstructed image when using many subsets for OS acceleration. For light field reconstruction, considering decomposing the camera imaging process into a linear convolution and a non-linear slicing operations for faster forward projection, we propose to reconstruct light field from a sequence of photos taken with different focus settings, i.e., a focal stack, using an alternating direction method of multipliers (ADMM). To improve the quality of the reconstructed light field, we also propose a signal-independent sparsifying transform by considering the elongated structure of light fields. Flatland simulation results show that our proposed sparse light field prior produces high resolution light field with fine details compared with other existing sparse priors for natural images.