Level-Set Method for Limited-Data Reconstruction in CT using Dictionary-Based Compressed Sensing

Compressed sensing using a dictionary is known to be effective for reconstructing CT images from incomplete projection data (eg. limited-angle CT and sparse-view CT) and its practical applications are increasing. However, when the measurement conditions are insufficient, its performance in image quality is still insufficient and the computational time is long. In this paper, to overcome these limitations, we propose a new method that can dramatically improve the performance by using a priori knowledge about the gray levels of the image to be reconstructed. But, the main problem with using prior information is that a standard formulation leads to a non-convex optimization problem that is difficult to solve. In this study, we succeeded in overcoming this problem based on deep theoretical consideration. Specifically, we formulate a convex optimization problem that can be stably and successfully solved based on an image model that expresses the boundary of the images as a level-set function consisting of linear combinations of the dictionary elements. We create the dictionary that determines the performance by preparing a small number of basic shapes followed by applying the geometric transformations to each shape to construct the dictionary elements. The simulation results for synthetic images and real data shown that the proposed method compared favorably to Total Variation, DART and Dual problem.