MRI Reconstruction Using Low-Rank Prior Of Nonlocal Similarity Patches

Magnetic resonance imaging (MRI) technology is a Medical diagnostic technology, which can obtain detailed diagnostic images of organs and tissues in vivo. MRI has been widely used in clinical and sometimes becomes an indispensable means of checking disease diagnosis. However, MRI takes a long time to obtain K-space data, In order to reduce the imaging time, there are two main method at present:one is to improve the hardware, such as multi coil parallel imaging and fast imaging gradient sequence design; another is to down sample K-space data, that is to sample partial K-space data and reconstruct the MR image using reconstruction methods. The partial K-space reconstruction methods attracts most attentions as it needn’t to change the existing equipments. Sparse representation and compressed sensing theory allows the accurately MR images reconstruction from only a few K-space data.In this paper, we follow the sparse representation and compress sensing method to reconstruct the low sampling rate K-space data.The reconstruction of partial K-space data is essentially an inverse problem, and the key of an inverse problem is the use of prior information. The conventional compress sensing based MRI reconstruction methods use a specific transform or an adaptive dictionary learning method to exploit the sparsity of the MR image. In this article, we make full use of the non-local similarity of MR image blocks to form low rank matrix for data reconstruction from part of the K-space data. The main work of this paper is shown as follows:First, we establish an low rank prior of nonlocal similarity patches based image denoising model. The MRI reconstruction can also summarize as an iteration of denoising problem, and the denoising problem is a simple inverse problem.In this article we establish an objective function to use the prior of nonlocal similarity and the low rank property of nonlocal similarity image patches. We also conduct a threshold denoising method, which is deferent from other threshold algorithm, all eigenvalues have a corresponding threshold. This model is applied to natural image denoising and MRI image denoising. The experiments show that the proposed denoising method has good denoising effect.Second, we construct low rank based MRI reconstruction model. Using alternating direction multiplier method to shift the objective function to an iteration of two problem:an image denoising problem and a least square problem. Apply the proposed image denoising model to MRI reconstruction model and give a closed solution for least square. The tests of actual MRI data show that the proposed method has strong ability to keep the details of the MR images. And the compare experiments with other methods also show that the proposed method can better reconstruct the MR images from partial K space data.