Magnetic resonance image reconstruction from undersampled measurements using a patch-based nonlocal operator

Compressed sensing MRI (CS-MRI) has shown great potential in reducing data acquisition time in MRI. Sparsity or compressibility plays an important role to reduce the image reconstruction error. Conventional CS-MRI typically uses a pre-defined sparsifying transform such as wavelet or finite difference, which sometimes does not lead to a sufficient sparse representation for the image to be reconstructed. In this paper, we design a patch-based nonlocal operator (PANO) to sparsify magnetic resonance images by making use of the similarity of image patches. The definition of PANO results in sparse representation for similar patches and allows us to establish a general formulation to trade the sparsity of these patches with the data consistency. It also provides feasibility to incorporate prior information learnt from undersampled data or another contrast image, which leads to optimized sparse representation of images to be reconstructed. Simulation results on in vivo data demonstrate that the proposed method achieves lower reconstruction error and higher visual quality than conventional CS-MRI methods.