Compressively Sampled MRI Recovery Using Modified Iterative-Reweighted Least Square Method

Magnetic resonance imaging (MRI) is a medical imaging modality used for high-resolution soft-tissue imaging of human body. In traditional MRI acquisition methods, sampling is performed at Nyquist rate to store data in k-space. The MR image is recovered using inverse Fast Fourier Transform (FFT). This approach results in slow data acquisition process, which is uncomfortable for the patients. Compressed Sensing (CS) acquisition approach offers nearly perfect recovery of MR image using non-linear reconstruction algorithms even from partial k-space data. This study presents a novel method to reconstruct MR image from highly under-sampled data using modified Iterative-Reweighted Least Square (IRLS) method with additional data consistency constraints. IRLS is an effective numerical method used in convex optimization problems. The proposed algorithm was applied on original human brain and Shepp–Logan phantom image, and the data acquired from the MRI scanner at St. Mary’s Hospital, London. The experimental results show that the proposed algorithm outperforms Projection onto Convex Sets (POCS), Separable Surrogate Functional (SSF), Iterative-Reweighted Least Squares (IRLS), Zero Filling (ZF), and Low-Resolution (LR) methods based on the parameters, e.g. Peak Signal-to-Noise Ratio (PSNR), Improved Signal-to-Noise Ratio (ISNR), Fitness, Correlation, Structural SIMilarity (SSIM) index, and Artifact Power (AP).