Magnetic resonance imaging (MRI) reconstruction from undersampled data has always been a challenging and fascinating task due to its implicit ill-posed nature and its significance accompanied with the emerging compressed sensing (CS) theory.Most state-of-the-art sparse representation based CS approaches partition the image into overlapped patches,and process each patch separately.These methods,however,lose important spatial structures of the signal of interest,and ignore the consistency of pixels,which is a strong constraint for MR image.In this paper,we propose a new reconstruction method,which builds on recently introduced ideas of convolutional sparse coding in gradient domain (GradCSC) to address above mentioned issue.As opposed to patch-based methods,GradCSC directly operates on the whole gradient image to capture the correlation between local neighborhoods and exploits the gradient image global correlation to produce better edges and sharp features of gradient image.It enables local features implicitly existed in the gradient images to be captured effectively.Extensive experimental results demonstrate that the proposed algorithm achieves higher quality reconstructions than alternative methods and converges quickly at various sampling schemes and k-space acceleration factors
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