Super-resolution MRI images using Compressive Sensing

Compressive Sensing (CS) is a new method for sparse images reconstruction using incomplete measurements. In this study our goal is to reconstruct a High Resolution (HR), MR image from a single Low Resolution (LR) image. Our proposed method applies the CS theory to Super Resolution (SR) single Magnetic Resonance Imaging (MRI). We first use a LR image generated by applying a Gaussian filter on the original image (for k-space under-sampling) and then generate the HR image by using CS theory. The formulation of CS theory emphasizes on maximizing image sparsity on known sparse transform domain and minimizing fidelity. For satisfying sparsity, finite difference is applied as a sparsifying transform. We propose and compare the Non-Linear Conjugate Gradients (NLCG) and Split Bregman (SB) algorithms as two different image reconstructing methods in CS. The result images are compared with three types of images: Original image which is used as the input of experiments, low quality of original image and the image which is generated by Zero Filling (ZF) algorithm. The following measures are used for evaluation: SNR, PSNR, SSIM and MSE. Experiments show that the SB algorithm outperforms ZF and NLCG for reconstructing MR images.