Compressed sensing based cone-beam computed tomography reconstruction with a first-order method

Purpose: This article considers the problem of reconstructing cone-beam computed tomography (CBCT) images from a set of undersampled and potentially noisy projection measurements. Methods: The authors cast the reconstruction as a compressed sensing problem based on l₁ norm minimization constrained by statistically weighted least-squares of CBCT projection data. For accurate modeling, the noise characteristics of the CBCT projection data are used to determine the relative importance of each projection measurement. To solve the compressed sensing problem, the authors employ a method minimizing total-variation norm, satisfying a prespecified level of measurement consistency using a first-order method developed by Nesterov. Results: The method converges fast to the optimal solution without excessive memory requirement, thanks to the method of iterative forward and back-projections. The performance of the proposed algorithm is demonstrated through a series of digital and experimental phantom studies. It is found a that high quality CBCT image can be reconstructed from undersampled and potentially noisy projection data by using the proposed method. Both sparse sampling and decreasing x-ray tube current (i.e., noisy projection data) lead to the reduction of radiation dose in CBCT imaging. Conclusions: It is demonstrated that compressed sensing outperforms the traditional algorithm when dealing with sparse, and potentially noisy, CBCT projection views.