Coherence regularization for SENSE reconstruction with a nonlocal operator (CORNOL).

The sensitivity encoding (SENSE) reconstruction reconstruction of parallel imaging can suffer from amplified noise at high reduction factors due to the ill-conditioned system matrix. Regularization alleviates this problem by imposing priors on the reconstructed image. These priors typically introduce both intrastructure smoothness and interstructure smoothness. The former mainly reduces noise, while the latter can also decrease intensity changes between different structures and cause structure loss. In this study, coherence regularization was proposed to impose only intrastructure smoothness in order to enhance the preservation of the image structure. Its energy functional was formed by examining the connection between regularization and the diffusion equation of adaptive image filtering. The coherence regularization extracts image structure information directly from the noisy data by adapting diffusion equation-related image-filtering methods. In this study, a nonlocal operator derived from the nonlocal mean filter was used for structure detection. Based on this structure information, only intrastructure intensity changes are penalized while the interstructure intensity changes are preserved. Both phantom simulation and in vivo experiments demonstrate that the coherence regularization would be able to effectively suppress noise in SENSE reconstruction at high reduction factors while suffering from much less image degradation, compared to Tikhonov and total variation methods.