A base function expressed with Chebyshev polynomials is reached. The relationship between the coefficients of the partial differential equation and the base function is deduced. Using the relationship, one can obtain ...A base function expressed with Chebyshev polynomials is reached. The relationship between the coefficients of the partial differential equation and the base function is deduced. Using the relationship, one can obtain nearly the same results as those calculated by Fast Fourier Transformation (FFT). The pseudo-spectral matrix method is applied in this paper to simulate numerically the incompressible laminar boundary flow on a plate. The simulation proves to be precise and efficient.展开更多
针对超声衍射层析成像传统采用的双线性插值法重建精度不高的问题,提出一种高精度的核卷积插值重建算法.首先,根据标准的sheep and Logan体模算出重建数据点的值,再选用最小二乘非均匀快速傅里叶变换(LS-NUFFT)算法里的核矩阵作为卷积核...针对超声衍射层析成像传统采用的双线性插值法重建精度不高的问题,提出一种高精度的核卷积插值重建算法.首先,根据标准的sheep and Logan体模算出重建数据点的值,再选用最小二乘非均匀快速傅里叶变换(LS-NUFFT)算法里的核矩阵作为卷积核,并用此核矩阵将非笛卡儿分布的重建数据点插值到笛卡儿网格内,最后用二维的傅里叶逆变换完成图像的重建.与双线性插值法和高斯核卷积法相比较,LS-NUFFT核矩阵法所得重建图像的2-范数误差比双线性法减少了40%以上,重建时间比高斯核卷积法减少约50%.展开更多
文摘A base function expressed with Chebyshev polynomials is reached. The relationship between the coefficients of the partial differential equation and the base function is deduced. Using the relationship, one can obtain nearly the same results as those calculated by Fast Fourier Transformation (FFT). The pseudo-spectral matrix method is applied in this paper to simulate numerically the incompressible laminar boundary flow on a plate. The simulation proves to be precise and efficient.
文摘针对超声衍射层析成像传统采用的双线性插值法重建精度不高的问题,提出一种高精度的核卷积插值重建算法.首先,根据标准的sheep and Logan体模算出重建数据点的值,再选用最小二乘非均匀快速傅里叶变换(LS-NUFFT)算法里的核矩阵作为卷积核,并用此核矩阵将非笛卡儿分布的重建数据点插值到笛卡儿网格内,最后用二维的傅里叶逆变换完成图像的重建.与双线性插值法和高斯核卷积法相比较,LS-NUFFT核矩阵法所得重建图像的2-范数误差比双线性法减少了40%以上,重建时间比高斯核卷积法减少约50%.
