A tensor PRISM algorithm for multi-energy CT reconstruction and comparative studies

Abstract

Different from the single-energy CT (SECT), multi-energy CT (MECT) acquires projection data at different energy spectra, which makes that the MECT has more sparsity among the data of separate energy and over energy. In order to maximize utilization of all these sparse characteristics, this paper proposed a new tensor PRISM model to consistently treat a priori knowledge of the low rank, intensity and sparsity with the higher-dimensional tensor technique. The priori knowledge of low rank corresponds to the stationary background and similarity over the energy, and the intensity and sparsity represents the rest of image features at single energy. Then, the regularization and convex minimization problem was solved by tensor unfolding and an extended tensor-based split-Bregman algorithm. Different from the previous PRISM algorithm, the new algorithm mixed and treated different constraints consistently. Numerical experiments have shown that our tensor PRISM approach performs much better than the popular $l_{1}$ regularization algorithm in terms of image quality for MECT.