基于Bregman迭代的CT图像重建算法

针对大规模集成电路领域CT重建图像的特点,提出TV约束条件下采用l1范数作正则项的重建模型,并给出了基于Bregman迭代的模型求解算法.算法分为两步: 1)采用Bregman迭代求解图像的l1范数作为正则项,误差的加权l2范数作为保真项的约束极值问题;2) 采用TV约束对1)中得到的重建图像进行修正.算法对TV约束条件下采用l1作正则项的重建模型分开求解,降低了算法的复杂度,加快了收敛速度.算法在稀疏投影数据下可以快速重建CT图像且质量较好.本文采用经典的Shepp-Logan图像进行仿真实验并对实际得到的电路板投影数据进行重建,结果表明该算法可满足重建质量要求且重建速度有较大提升.

Reconstruction Algorithm Based on Bregman Iteration

In this paper, we present a new reconstruction model based on l₁ regularization and TV constraint conditions in the large scale integrated circuit field. And then, we give the new reconstruction algorithm to the new model based on Bregman iteration. The new algorithm consists of two steps. 1) We take the l₁-norm of image as the regularization item and weighted l₂-norm of image error as the fidelity item, and solve this constrained optimization problem using the Bregman iteration; 2) We make further improvement using TV constraint to the reconstructed image obtained by Step 1). The new algorithm separates the above two steps, so, it reduces the complexity of the algorithm and accelerates the convergence rate. In the end, we apply the new algorithm to the classic Shepp-Logan mode and a circuit board image. Experimental results show that the advantage of the new algorithm on reconstruction speed is obvious and the reconstruction quality is good.