定步长压缩感知锥束CT重建算法  

Compressing-sensing cone-beam CT reconstruction algorithm of fixed step-size

作　　者：张晓梦[1,2,3] 杨宏成[1,2,3] 张涛[2] 

机构地区：[1]中国科学院苏州生物医学工程技术研究所,江苏苏州215163 [2]中国科学院长春光学精密机械与物理研究所,长春130000 [3]中国科学院大学,北京100049

出　　处：《计算机应用》2014年第2期553-557,共5页journal of Computer Applications

基　　金：国家科技支撑计划项目(2012BAI13B00);国家重大科学仪器设备开发专项(2011YQ040082)

摘　　要：针对锥束CT成像系统中投影数据不完全的图像重建问题,提出了一种定步长压缩感知锥束CT重建算法。首先将锥束CT重建问题归结为投影数据均方误差作为数据保真项、全变分作为正则项的无约束优化问题,分析目标函数的Lipschitz连续性;然后近似计算Lipschitz常数,求出梯度下降步长,利用梯度下降法进行重建;最后对CT投影数据采用联合代数重建算法更新重建图像。在每次迭代过程中调整梯度下降步长,提高重建算法的收敛速度。Shepp-Logan模型的无噪声实验结果表明,该算法的重建图像信噪比分别比联合代数重建算法、自适应最速下降-凸集投影算法、BB梯度投影算法的重建图像信噪比高出13.7728 dB、12.8205 dB、7.3580 dB。仿真试验表明该重建算法提高了收敛速度,同时减少了重建图像的相对误差,极大提高了用少量投影数据重建的图像质量。To solve the problem of image reconstruction of incomplete projection data from cone-beam CT, a fast cone- beam CT reconstruction algorithm was proposed. In this work, the cone-beam CT reconstruction problem was reduced to an unconstrained optimization problem of minimizing an objective function which included a squared error term combined with a sparseness-inducing regularization term. The Lipschitz continuity of the objective function was analyzed and the Lipschitz constant was estimated based on its definition. The gradient descent step-size was calculated by the Lipschitz constant and the reconstructed image was updated by gradient method. Finally simultaneous algebraic reconstruction technique was used to reconstruct image from limited-angle projections and to meet the constraint of the projection data. An adaptive step-size technique was accommodated as so to accelerate the convergence of proposed algorithm. Simulation with noiseless Shepp-Logan shows： In comparison with simultaneous algebraic reconstruction technique, adaptive steepest descent-projection onto convex sets algorithm and gradient-projection Barzilari-Borwein algorithm, the proposed algorithm has higher SNR （Signal-to-Noise Ratio） by 13.7728 dB, 12. 8205 dB, and 7. 358 0 dB respectively. The algorithm has better performance in convergence speed and reconstruction accuracy, and can greatly improve the quality of images reconstructed from few projection data.

关 键 词：压缩感知 定步长 锥束CT 图像重建 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]