低剂量CT的线性Bregman迭代重建算法

Linearized Bregman Iterations for Low-dose CT Reconstruction

针对降低X线源管电流来减少辐射剂量的实现方案所引起的投影图像低信噪比的情况,该文提出一种新的低剂量CT图像重建模型。总的优化目标函数采用泊松噪声的负对数似然函数作为数据保真项,采用待重建图像的稀疏性先验信息作为正则项。保真项能够克服加性高斯模型不能有效刻画噪声性质的缺点,正则化项能够改善测量低信噪比所引起的不适定性。求解过程中采用线性化Bregman迭代格式,将原目标函数分解为变系数的2次优化问题和稀疏性先验去噪问题,其中的2次优化问题中的2次项系数采用变系数计算,能够更好地逼近原始的保真项,从而加快收敛速度。在低剂量扇形束成像的条件下,对仿真模型进行了数值试验,并同传统的滤波反投影算法、极大似然算法和加权2范数重建算法进行了比较,验证了该文算法的有效性。

A new low dose CT reconstruction model is proposed under the condition of low signal-to-noise ratio measured data, which are caused by reducing the X-ray source tube current in order to avoid the excessive radiation dose. In the objective function of the model, the logarithm likelihood function under Poisson noise is used as the fidelity functional, and sparse prior of image transform domain coefficients is used as the regularization functional. The fidelity functional is more effective than the additive Gaussian noise model, while the regularization the functional can overcome the ill posed problem of image reconstruction expecially in the low-dose situation. By using the linearized Bregman iteration, the sum minimization scheme is split into one step of quadratic programming with variable coefficient and the other step of the denoising issue. It can accelerate the convergence speed through the variable coefficient calculation in the quadratic programming to approximate the original fidelity term. Experimental results show that this proposed approach can be successfully applied to low-dose fan-beam CT reconstruction and it outperforms some existing algorithms including filter back projection algorithm, maximum likelihood algorithm and classical weighted l2 norm reconstruction algorithm.