Exploiting rank deficiency for MR image reconstruction from multiple partial K-space scans

In Magnetic Resonance Imaging (MRI) the acquired K-space data is corrupted by white Gaussian noise or by motion artifacts. In order to reduce the effects of these factors, it is a common practice to take multiple scans of the K-space. Noise/motion artifacts are reduced by averaging the K-space scans. For fully scanned K-space data, the image is obtained from this averaged K-space by applying the inverse Fourier transform. However, sampling the full K-space is time consuming. To reduce the scan-time smart reconstruction algorithms are employed obtain the MR image partial K-space scans. Generally Compressed Sensing (CS) based techniques are used to this end. In this work, we will show how the image can be reconstructed from multiple partial K-space scans by nuclear norm minimization. The reconstruction accuracy from our proposed method is the same as CS based techniques but is about ten times faster.