Locally linear constraint based optimization model for material decomposition

Dual spectral computed tomography (DSCT) has a superior material distinguishability than the conventional single spectral computed tomography (SSCT). However, the decomposition process is an illposed problem, which is sensitive to noise. Thus, the decomposed image quality is degraded, and the corresponding signal-to-noise ratio (SNR) is much lower than that of directly reconstructed image of SSCT. In this work, we establish a locally linear relationship between the decomposed results of DSCT and SSCT. Based on this constraint, we propose an optimization model for DSCT and develop an iterative method with image guided filtering. To further improve the image quality, we employ a preprocessing method based on the relative total variation regularization. Both numerical simulations and real experiments are performed, and the results confirm the effectiveness of our proposed approach.