层析成像图像重建算法综述

介绍了层析成像技术的图像重建算法,并从正向问题数学模型的简化和反向问题数学模型的映射结构的角度比较了各种算法的特点和优劣。研究表明:用本质是线性算法的各种变换方法重建图像存在严重失真,而卷积滤波的引入可以使变换方法的重建效果有所改善;基于导数搜索的迭代算法对初始值依赖性强、收敛速度慢并且容易陷入局部最优解;基于Fourier变换的方法具有本质的局限性;小波变换则可以同时刻画图像时域和频域的细节特征;有限元法通过重建对象像素的智能划分可以简化正问题的复杂性;而具有物理背景的蒙特卡罗法、模拟退火法、遗传算法、粒子滤波法及神经网络法更适合于复杂且非线性的图像重建;智能化、仿生化、并行化以及各种算法的融合是层析成像图像重建算法的发展趋势。

Image reconstruction algorithms of computed tomography

The image reconstruction algorithms of tomography are introduced. The characteristics of the various algorithms are compared from the points of view of the forward model simplication and reverse model mapping structure. Studies show that the various conversion methods belonging to linear algorithm have serious distor- tion, which can be improved by convolution filtering. The various iterative algorithms based on derivative search have strong initial value dependence and slow convergence and are easy to fall into a local optimal solu- tion. The various Fourier transform methods have intrinsic limitation and the wavelet transform can characterize both the time and frequency domain minutiae of the image. The finite element method can simplify the forward model by smart designing pixels of the reconstruction object. With the physical background, the Monte Carlo method, simulated annealing, genetic algorithms, particle filter method and the neural network method are more suitable for complex and nonlinear image reconstruction. Moreover, intelligentization, modeling, paral- lelization, and integration of various algorithms are the trends for the image reconstruction algorithms of the tomography.