定步长压缩感知锥束CT重建算法

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13.7728dB、12.8205dB、7.3580dB。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。

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

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 13.7728dB, 12.8205dB, and 7.3580dB 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.