Multi-energy CT reconstruction based on Low Rank and Sparsity with the Split-Bregman Method (MLRSS)

With the development of computed tomography (CT), the classical grayscale CT will become multi-energy CT in the future, which will provide richer information. In this paper, we will discuss a new method called Combination of Low Rank and Sparsity with the Split-Bregman Method (CLRSS), which performs well when we treat the Multi-Energy CT images as a tensor and do the image reconstruction. Image reconstruction is in fact a process of iteration and optimization. In the process, CLRSS will utilize images' characteristics known to us. The first characteristic is the similarity with the origin signals, which is the foundation of our image. The second characteristic is low rank in tensor unfolding, which could be described by trace norm and solved with the singular value decomposition (SVD). The third characteristic is the sparsity in a certain transform, and we use TV norm to describe the sparsity. Furthermore, with the help of the Split-Bregman method, it is possible to combine the characteristics together and solve the optimization problem. Finally we will see the superior performance of CLRSS in the reconstruction with insufficient information.