Sampling Density Compensation Function Estimation by Regularized Conjugate Gradient Iteration with a Reduced Oversampling Ratio

Sen Jia¹, Ran Yang¹

The iterative convolution based estimation of non-Cartesian sampling density compensation function (DCF) typically employs an intermediate Cartesian grid oversampled by a ratio of two to achieve high convergence accuracy and this increases the memory and computational burden heavily when processing data of large size or of high dimension. And the iteration converges stably but saturates easily which limits the capacity to achieve higher estimation accuracy. In this work, an iterative procedure based on the Conjugate Gradient (CG) method is introduced to reduce the oversampled grid size while achieving higher DCF estimation accuracy without increasing computational and storage burden. Further the DCF estimated by the original method is employed as a regularization term to form a bi-criterion optimization problem to stabilize the CG iteration to achieve fast convergence with a reduced oversampling ratio.