光学学报, 2018, 38(1): 0111003, 网络出版: 2018-01-01

角度受限下稀疏投影数据的改进粒子群优化随机CT重建

Improved Stochastic CT Reconstruction Based on Particle Swarm Optimization for Limited-Angle Sparse Projection Data
作者单位

1华南理工大学自动化科学与工程学院, 广东 广州 510640

2广州大学机械与电气工程学院, 广东 广州 510006

摘要
当计算机断层成像(CT)中X射线的采样范围和数量受限时,得到的稀疏投影数据完备性很低,重建算法的搜索空间巨大。基于凸优化思路的迭代求解算法及其改进采用固定搜索路径,难以在有限时间内收敛至全局最优解;粒子群优化具有全局搜索能力,但计算成本和存储代价过高。为解决这类不完备投影数据的重建问题,提出基于粒子群优化的随机稀疏重建算法。首先,通过随机策略生成具有多样性的初始种群,以保证算法的搜索能力;其次,随机选择梯度下降或基于个体历史最优解和全局历史最优解的随机方向进行迭代,以兼顾算法效率和搜索方向的多样性;最后,基于适应度评价,有针对性地重新生成随机初始种群,强制跳离局部最优。针对角度受限下无噪声和含噪声的稀疏投影数据,分别进行重建实验。结果显示,与常见的凸优化迭代和粒子群优化算法相比,本文算法既能保证算法效率,又在重建质量和算法稳健性上具有明显优势。
Abstract
Because of the sampling scope and quantity limitation in the computed tomography (CT), the completeness of sparse projection data is very low, which leads to a huge search space for the reconstruction algorithm. The iterative algorithm based on convex optimization can not converge to the global minima in finite time due to the fixed search path. Particle swarm optimization has global search capability, but costs tremendous computation and memory. To improve the quality of reconstruction from incomplete projection data, a new stochastic sparse reconstruction algorithm based on particle swarm optimization is proposed. Firstly, the initial solutions with diversity are generated by the stochastic strategy to ensure the search capability. Secondly, the proposed algorithm stochastically chooses either gradient descent direction or random direction based on the local best known solution and the global best known solution in the iteration, to ensure the efficiency of this algorithm and the diversity of search directions. Finally, to avoid trapping in local optimum, the random initial populations are generated based on the fitness evaluation, which represents the current situation. The contrast reconstruction experiments are conducted on both noise-free and noisy limited-angle sparse projection data. The experimental results demonstrate that the proposed algorithm is efficient and evidently superior in reconstruction quality and robustness compared to common iterative algorithms based on convex optimization or particle swarm optimization.
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