Exploiting Sparsity and Rank Deficiency for MR Image Reconstruction From Multiple Partial K-Space Scans

In magnetic resonance imaging, it is a common to acquire multiple scans of the K-space so that the effects of noise and motion artifacts can be reduced by averaging the K-space scans. However, sampling the full K-space is time consuming; to reduce the scan time, compressed sensing (CS)-based reconstruction algorithms are employed to recover images from partially sampled K-space scans. A recent study showed that the recovery can also be achieved by exploiting the rank deficiency of the underlying images. In this paper, we will show how the reconstruction can be further improved by combining CS techniques with low-rank recovery methods. Our proposed formulation leads to a least-square minimization problem that is regularized by an ℓ₁-norm and a nuclear norm. There is no efficient and accurate algorithm to solve this problem; therefore, we derive an algorithm to solve the said problem based on the Split Bregman approach. The results show that our proposed technique reduces the reconstruction error by about 40%.