Preliminary Study: an Efficient Solving Algorithm for Determining the Exact Sampling Condition of Limited-Angle CT Reconstruction

In X-ray computed tomography (CT), it has been widely accepted that reconstruction methods inspired by compressive sensing (CS) can recover the image from an apparent reducing projection number. However, the quantitative study of sufficient sampling number of accurate reconstruction has high computational complexity, and it is limited by the size of the phantom. In this work, sampling condition of limited-angle accurate reconstruction is studied by testing the solution uniqueness in total variation (TV) minimization model. Solution uniqueness is verified by solving the l1 -norm minimization problem. To solve the problem and improve the efficiency, we propose a fast algorithm which is based on the alternating direction method of multipliers (ADMM). In the limited-angle problem, the proposed method quantifies the number of projection acquisitions for accurate reconstruction. The experimental results indicate that the proposed method is more computationally efficient than the existing method. And our method can reduce the limit of phantom size because the computational cost of our algorithm is approximately equivalent to the same size reconstruction problem.