Multichannel compressed sensing MR image reconstruction using statistically optimized nonlinear diffusion

Purpose Eliminate the need for parametric tuning in total variation (TV) based multichannel compressed‐sensing image reconstruction using statistically optimized nonlinear diffusion without compromising image quality. Theory and Methods Nonlinear diffusion controls the denoising process using a contrast parameter that separates the gradients corresponding to noise and true edges in the image. This parameter is statistically estimated from the variance of combined image gradient to yield minimum steady‐state reconstruction error. In addition, it uses acquired k‐space data to bias the diffusion process toward an optimal solution. Results The proposed method is compared with TV using a set of noisy spine and brain data sets for three, four, and five‐fold undersampling. It is observed that the choice of regularization parameter (step size) of TV‐based methods requires prior tuning based on an extensive search procedure. In contrast, statistical estimation of contrast parameter removes this need for tuning by adapting to the changes in data sets and undersampling levels. Conclusions Although an a‐priori tuned TV‐based reconstruction can provide a comparable image quality to that of controlled nonlinear diffusion, there are practical limitations with regard to its time complexity for ad‐hoc applications to multicoil compressed‐sensing reconstruction. Magn Reson Med 78:754–762, 2017. © 2017 International Society for Magnetic Resonance in Medicine