Fourier imaging in MRI application has the dilemma that using extended k-space sampling to improve image resolution 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 enforcing anatomical prior information is proposed

where directional regularization operators apply to the smooth areas

neighboring 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.