Bi-component decomposition based hybrid regularization method for partly-textured CS-MR image reconstruction

• Our method utilizes different regularization terms for cartoon and texture components.
• Our method can eliminate aliasing effect and preserve edges/textures efficiently.
• Our alternating direction method based algorithm can solve the new model efficiently.
• Our method can improve visual quality, PSNR and SSIM efficiently.

For compressive sensing magnetic resonance (CS-MR) image reconstruction, it is vital to preserve edges and textures while eliminating aliasing artifacts. The total variation (TV) regularization preserves edges well but causes staircase effect and fails to preserve textures. The high-order regularization can eliminate the staircase effect but causes edge blurring. The nonlocal TV (NLTV) regularization can preserve textures well, but causes extra artifacts and is likely to preserve the texture-like artificial structures caused by aliasing artifacts mistakenly. In this paper, we assume that the image consists of cartoon component and anisotropic component. For the cartoon component, we utilize the fractional-order TV regularization to eliminate the staircase effect and avoid edge blurring, and more importantly, we can avoid its disadvantage in texture preservation because there are no textures in the cartoon component. We utilize the NLTV regularization and the shearlet based sparsity regularization for the anisotropic component with piecewise-constant background. Without the effect of intensity inhomogeneity, the NLTV regularization can avoid preserving the texture-like artificial structures while preserving the real edges. The shearlet based sparsity regularization can provide further improvement of the image quality. Numerical experiments demonstrate that our method can eliminate the aliasing artifacts and preserve the edges and textures efficiently.