Blind Separation Model of Multi-voltage Projections for the Hardening Artifact Correction in Computed Tomography. (February 2021) - Wei, Jiaotong; Chen, Ping; Han, Yan; Zhao, Yaoxia
Abstract: The hardening artifacts caused by polychromatic X-ray beams in computed tomography (CT) reconstructed images increase the difficulty of quantitative analysis. A method based on the blind separation of multi-voltage projections is proposed to correct the hardening artifacts. Compared to most correction methods, this method does not require prior knowledge of the X-ray spectrum or materials or segmentation, reprojection or multiple reconstructions. The core concept of the method is to decompose the polychromatic X-ray projections to obtain projections with a narrow energy interval. The polychromatic X-ray projections can be seen as the sum of projections with narrow energy intervals. The multi-voltage projection matrix is decomposed into three matrixes. Since the X-ray beam is exponentially attenuated, two of the three matrixes are in the exponential term. The decomposition is an expanded form of nonnegative matrix factorization. Because the X-ray scatter is a low-frequency signal, the objective function of the decomposition model is the sum of the variance of the residual projection at different angles. The iterative solution formula can be derived under Karush-Kuhn-Tucker (KKT) optimality conditions. In experiments with real samples, the hardening artifacts are reduced compared to those in directly reconstructed images, demonstrating the availability of the proposed method.