中文摘要：

传统磁共振（MR）傅里叶成像方法由于傅里叶不确定性，k空间扩展编码采样长度能提高图像空间分辨率，但是以降低图像信噪比为代价。提出基于最大似然优化模型的各向异性约束MR成像新方法，将离散傅里叶变换模型改进为惩罚约束函数的最优值搜索问题。利用医学结构的先验信息，将正则化惩罚运算细化至平滑区域、边界邻域、边界和边界的方向。实验结果表明，该方法不但能扩展k空间高频数据采样长度同时有效降低高斯噪声，而且能克服现有相关约束成像方法的二次模糊和Gibbs环状伪影。

英文摘要：

Fourier imaging in MRI application has the dilemma that using extended k-space sampling to improve image reso- lution also degrades the signal-to-noise ratio （SNR） because of the Fourier uncertainty. In this paper, we propose a new method using anisotropically constrained image reconstruction based on a penalized maximum likelihood optimality model, which is an optimization problem instead of a discrete Fourier transform （DFT） approach. Anisotropic regularization for en- forcing anatomical prior information is proposed, where directional regularization operators apply to the smooth areas, neigh- boring edge areas and edges respectively. Experimental results show that the proposed method enables extended k-space sampling while suppressing Gaussian noise and reducing the reblurring problem and the Gibbs ringing artifacts of existing constrained reconstruction methods.