Image Reconstruction Algorithm With Incomplete Projection Data

Computed tomography(CT) is extensively applied in industrial, medical and security check areas for its advantages of nondestructive, high precision and threedimensional visualization. CT image reconstruction is a process of getting the slice image from its projection data. Image reconstruction algorithm is divided into analytical reconstruction algorithm and iterative reconstruction algorithm. Aiming at the image reconstruction problem from limited angle and sparse angle of micro CT, this paper studies the iterative reconstruction method with incomplete projection data.Aiming at the construction problem with incomplete data, we applies the SART(Simultaneous Algebraic Reconstruction Technique) iterative algorithm to reconstruct the image at first. In the iterative reconstruction algorithm, computing the weight coefficient matrix is the key link, whose calculation method and accuracy influences the quality of the image. Thus, it is very necessary to analyze and compare the construction image with different weight coefficient matrices. This paper studies the computing method of different weight coefficient matrices, and compares the construction image with different weight coefficient matrices, on the condition of complete and incomplete projection data respectively, such as the 0-1 method, distance driven method, Ray-Box Intersection method and the bilinear interpolation method. Besides, we repairs the logical bug in the original version of Ray-Box Intersection method and proposes a optimization algorithm of Ray-Box Intersection method. The result shows that the construction result of the optimization algorithm of Ray-Box Intersection method is worse than the one of the bilinear interpolation method,but the optimization one is still better than 0-1 method and distance driven method in respect of the quality of the construction image. Plus, this article compares the four weight coefficient matrix computing method in terms of algorithmic logic, speed and the result, and makes a conclusion that the bilinear interpolation method has a Significant advantages over other method in respect of the algorithmic logic and speed, and there is the least shadow in the reconstruction image which is remarkably close to the original one.However, just using the SART iterative algorithm is not enough to reconstruct the image exactly with incomplete projection data, so we introduces the Total Variation Minimization(Total Variation Minimization, TVM)image reconstruction algorithm which is based on the compressive sensing principle. We compare the reconstruction result of the combination of the TVM and SART algorithm with just using the SART algorithm, and get the conclusion that the combination of the TVM and SART method has a better result which has less shadow and is more clear and smooth. Plus, this paper chooses the optimal parameter range of the relaxation factor in SART and TVM algorithm.In summary, this article mainly researches the iterative construction algorithm for complete projection data. Then, we improve the shortage of Ray-Box Intersection algorithm and put forward an optimized Ray-Box Intersection algorithm which has certain advantages over the original one. In plus, aiming at the incomplete complete projection data problem such as sparse sampling and limited angle, this paper compares the construction image conducted by the SART algorithm with the one conducted by the combination of TVM and SART algorithm.