An efficient compressive sensing MR image reconstruction scheme

Compressive sensing (CS) has great potential to reduce imaging time. It samples very few linear projections, and exploits sparsity or compressibility to reconstruct images from the measurements. Medical and most natural images usually contain various fine features, details and textures. Widely used total variation (TV) and wavelet sparsity are not so effective in reconstructing these images. We propose to incorporate total generalized variation (TGV) and shearlet transform to efficiently produce high quality images from compressive sensing MRI data, i.e., incomplete spectral Fourier data. The proposed model is solved by using split Bregman and primal-dual methods. Numerous numerical results on various data corresponding to different sampling rates and noise levels show the advantage of our method in preserving various geometrical features, textures and spatially variant smoothness. The proposed method consistently outperforms related competitive methods and shows greater advantage as sampling rate goes lower.