Optimization-based region-of-interest reconstruction for X-ray computed tomography based on total variation and data derivative

Region-of-interest (ROI) and interior reconstructions for computed tomography (CT) have drawn much attention and can be of practical value for potential applications in reducing radiation dose and hardware cost. The conventional wisdom is that the exact reconstruction of an interior ROI is very difficult to be obtained by only using data associated with lines through the ROI. In this study, we propose and investigate optimization-based methods for ROI and interior reconstructions based on total variation (TV) and data derivative. Objective functions are built by the image TV term plus the data finite difference term. Different data terms in the forms of L1-norm, L2-norm, and Kullback-Leibler divergence are incorporated and investigated in the optimizations. Efficient algorithms are developed using the proximal alternating direction method of multipliers (ADMM) for each program. All sub-problems of ADMM are solved by using closed-form solutions with high efficiency. The customized optimizations and algorithms based on the TV and derivative-based data terms can serve as a powerful tool for interior reconstructions. Simulations and real-data experiments indicate that the proposed methods can be of practical value for CT imaging applications.