Combining total variation with nonlocal self-similarity constraint for compressed sensing MRI

Undersampling k-space data is an efficient way to reduce the acquisition time of magnetic resonance imaging (MRI) technique. As a promising signal recovery method, compressed sensing (CS) is able to reconstruct magnetic resonance images using a few samples and therefore has great potential in speeding up MRI process. The traditional total variation (TV) based CS approaches tend to over-smooth local image details. This paper proposes an improved CS reconstruction method for MR images by combining local TV regularization, wavelet sparsity regularization and nonlocal (NL) self-similarity constraint together. The experimental results demonstrate that the local TV model and NL self-similarity constraint are complementary to each other, making the proposed approach highly effective in reducing noise and preserving image edges and details.