Compressed sensing MR image reconstruction based on nonlocal total variation and partially known support

By exploiting the similarity of the structure between the reference and the target images, a novel compressed sensing (CS)-based reconstruction method was proposed for MR image. Indexes of the L largest wavelet coefficients of the reference image were extracted and regarded as the known part of the desired target image's support, and the l₁ norm of the wavelet coefficients belonging to the complement to the known support was constrained. Furthermore, the nonlocal total variation (NLTV) was utilized as a regularization term to construct the objective function. Then the target image was reconstructed via a fast composite splitting algorithm (FCSA). Experimental results demonstrate that the proposed method can preserve edges and details while suppressing noise efficiently. It outperforms conventional CS-MRI and other similar reconstruction methods under the same sampling rate.