An evolutionary multi-criterion optimization approach utilizing the characteristics of strength distribution for sparse CT image reconstruction

In general, computed tomography (CT) tries to reconstruct a cross-section image by gathering projection data in multiple directions. However, there are several cases where angles of the projection have been strictly limited. In this case, the missing information should be estimated correctly in order to create a highly accurate reconstructed image. This problem is called "sparse CT" and known as one of the typical inverse problems. Since amount of information needed for reconstructing an image is missing, it needs to find several high quality solutions in order to estimate a true image. There have been several approaches proposed for solving this problem and they could achieve a certain result in the case of a low missing ratio problem, while there have been few approaches for the problem being large missing ratio. Therefore there is no established standard method for this problem. In this study, a new approach based on the Gerchberg-Saxton algorithm (GS algorithm) and evolutionary multi-criterion optimization (EMO) is proposed for sparse CT. The GS algorithm is known as a powerful technique for recovering the missing information in the field of phase retrieval problem. The proposed approach tries to find several solutions being high quality by using the framework of EMO. Also, the feature of our approach is not only the combination of GS and EMO, but also the implementation of genetic operators considering the characteristics of Fourier spectrum. Through applying to some typical images, the effectiveness of the proposed approach was investigated.