Edge-preserving reconstruction from sparse projections of limited-angle computed tomography using ℓ₀-regularized...

Accurate images reconstructed from limited computed tomography (CT) data are desired when reducing the X-ray radiation exposure imposed on patients. The total variation (TV), known as the l₁-norm of the image gradient magnitudes, is popular in CT reconstruction from incomplete projection data. However, as the projection data collected are from a sparse-view of the limited scanning angular range, the results reconstructed by a TV-based method suffer from blocky artifact and gradual changed artifacts near the edges, which in turn make the reconstruction images degraded. Different from the TV, the ℓ₀-norm of an image gradient counts the number of its non-zero coefficients of the image gradient. Since the regularization based on the ℓ₀-norm of the image gradient will not penalize the large gradient magnitudes, the edge can be effectively retained. In this work, an edge-preserving image reconstruction method based on l₀-regularized gradient prior was investigated for limited-angle computed tomography from sparse projections. To solve the optimization model effectively, the variable splitting and the alternating direction method (ADM) were utilized. Experiments demonstrated that the ADM-like method used for the non-convex optimization problem has better performance than other classical iterative reconstruction algorithms in terms of edge preservation and artifact reduction.