Volume Conservation Constrained Multi-Material Reconstruction for Inconsistent Spectral CT Imaging

Spectral computed tomography (spectral CT) is a promising medical imaging technology because of its ability to provide information on material characterization and quantification. However, the difficulty of decomposition also increases due to the nonlinearity nature of the measurements and ill condition of the problem, especially in the case of geometric inconsistency, which typically leads to low image qualities. Therefore, it is a crucial issue for inconsistent spectral CT imaging to improve the accuracy of material decomposition while suppressing the noise. This paper depends on a statistical reconstruction model with different priors to propose one-step multi-material algorithms. In these approaches, the gradient sparisty-based and convolutional neural network based methods are designed for the case of the consistent numbers of material and energies. And volume conservation constraint are further developed while the two numbers are not equal. An efficient Newton descent method is adopted based on the simple surrogate function. For simulation experiments with different noise levels, the largest peak signal-to-noise ratio (PSNR) obtained by the proposed method approximately increases by 20.924 dB and 18.283 dB compared with those of other algorithms. Magnified areas of real data also further demonstrated that the proposed methods has a better ability to suppress noise. Numerical experiments verify that the proposed method efficiently reconstructed the material maps, and reduced noise compared with the state-of-the-art methods.