摘要
为在迭代图像重建算法中获得更高质量的重建图像,推导出TV(Total Variation)正则化项关于重建图像的Fréchet导数,并给出该导数的有限元表示;利用两个数值实验,分别采用不同的网格尺寸和不同的形函数验证该有限元表示结果.数值实验结果表明:采用相同的k次单纯形元时,随着网格不断加密,计算结果的L1和L2误差均下降;采用相同的网格时,线性单纯形元函数计算结果明显优于分片常数有限元和二次单纯形元计算结果.
To get high quality reconstructed image in iterative algorithm of image reconstruction, the Frechet derivative of Total Variation （TV） regularization term with respect to reconstructed image is derived and then it is represented by finite element. The performance of the finite element representation is tested with two numerical experiment examples, into which different mesh sizes and different shape functions are introduced. The numerical experiment results show that, with the same k-th simplex shape element, L1 and L2 errors of the calculation results both decrease with the enhancement of mesh refinement degree; with the same mesh, the calculation results using linear simplex shape element are much better than the results using piecewise constant finite element and 2-nd simplex shape element.
出处
《计算机辅助工程》
2012年第3期49-52,56,共5页
Computer Aided Engineering
基金
上海海事大学校科研基金(20110054)
