The problem of potential field inversion can be become that of solving system of linear equations by using of linear processing. There are a lot of algorithms for solving any system of linear equations, and the regula...The problem of potential field inversion can be become that of solving system of linear equations by using of linear processing. There are a lot of algorithms for solving any system of linear equations, and the regularized method is one of the best algorithms. But there is a shortcoming in application with the regularized method, viz. the optimum regularized parameter must be determined by experience, so it is difficulty to obtain an optimum solution. In this paper, an iterative algorithm for solving any system of linear equations is discussed, and a sufficient and necessary condition of the algorithm convergence is presented and proved. The algorithm is convergent for any starting point, and the optimum solution can be obtained, in particular, there is no need to calculate the inverse matrix in the algorithm. The typical practical example shows the iterative algorithm is simple and practicable, and the inversion effect is better than that of regularized method.展开更多
针对Radon投影的计算机断层(Computer Tomography,CT)重建问题,提出了一种新的基于单位圆上正交展开法(Orthogonal Polynomial Expansions on the Disk,OPED)的有限角投影数据快速重建算法。该算法通过求解缺失投影与已知数据分别对应...针对Radon投影的计算机断层(Computer Tomography,CT)重建问题,提出了一种新的基于单位圆上正交展开法(Orthogonal Polynomial Expansions on the Disk,OPED)的有限角投影数据快速重建算法。该算法通过求解缺失投影与已知数据分别对应的正弦变换数据集之间所满足的线性方程组,得到完备数据正弦变换数据集的近似值,之后运用快速傅里叶变换(Fast Fourier Transform,FFT)及线性插值算法提高重建速度从而缩短重建时间。分别推导了单、双边投影数据缺失时的快速重建算法并给出了重建结果,实验结果证明,该方法能够有效提高重建效率。展开更多
基金the work is supported by scientific and technological fund of CNPC
文摘The problem of potential field inversion can be become that of solving system of linear equations by using of linear processing. There are a lot of algorithms for solving any system of linear equations, and the regularized method is one of the best algorithms. But there is a shortcoming in application with the regularized method, viz. the optimum regularized parameter must be determined by experience, so it is difficulty to obtain an optimum solution. In this paper, an iterative algorithm for solving any system of linear equations is discussed, and a sufficient and necessary condition of the algorithm convergence is presented and proved. The algorithm is convergent for any starting point, and the optimum solution can be obtained, in particular, there is no need to calculate the inverse matrix in the algorithm. The typical practical example shows the iterative algorithm is simple and practicable, and the inversion effect is better than that of regularized method.
文摘针对Radon投影的计算机断层(Computer Tomography,CT)重建问题,提出了一种新的基于单位圆上正交展开法(Orthogonal Polynomial Expansions on the Disk,OPED)的有限角投影数据快速重建算法。该算法通过求解缺失投影与已知数据分别对应的正弦变换数据集之间所满足的线性方程组,得到完备数据正弦变换数据集的近似值,之后运用快速傅里叶变换(Fast Fourier Transform,FFT)及线性插值算法提高重建速度从而缩短重建时间。分别推导了单、双边投影数据缺失时的快速重建算法并给出了重建结果,实验结果证明,该方法能够有效提高重建效率。
