MRI Reconstruction From Sparse K-Space Data Using Low Dimensional Manifold Model

Recent compressed sensing (CS) approaches to utilize the similarity and redundancy of magnetic resonance (MR) image patches to enable reconstruction from sparse k-space measurements. In this paper, the patches’ similarity and redundancy are exploited by applying the low-dimensional manifold model (LDMM). The basic assumption of the LDMM is that the image patches sample a manifold whose intrinsic dimensions are much lower than the high-dimensional ambient space. MR images also exhibit a low-dimensional patch-manifold structure. Based on this assumption, the dimension of the patch-manifold is used as a regularizer in a variational formulation. The MR image is then reconstructed by keeping the dimension of the patch manifold as small as possible. The proposed algorithm significantly increases the quality of the reconstructed images. The algorithm is evaluated on two datasets containing 100 MR images each. The reconstruction quality of the algorithm, gauged using three quality metrics: peak signal-to-noise ratio, structural similarity index measure, and normalized root-mean-square error, is better than the comparison methods.