Description: 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, 2017. © 2017 International Society for Magnetic Resonance in Medicine.

Description: Purpose Avoid formation of staircase artifacts in nonlinear diffusion-based MR image reconstruction without compromising computational speed. Methods Whereas second-order diffusion encourages the evolution of pixel neighborhood with uniform intensities, fourth-order diffusion considers smooth region to be not necessarily a uniform intensity region but also a planar region. Therefore, a controlled application of fourth-order diffusivity function is used to encourage second-order diffusion to reconstruct the smooth regions of the image as a plane rather than a group of blocks, while not being strong enough to introduce the undesirable speckle effect. Results Proposed method is compared with second- and fourth-order nonlinear diffusion reconstruction, total variation (TV), total generalized variation, and higher degree TV using in vivo data sets for different undersampling levels with application to dictionary learning-based reconstruction. It is observed that the proposed technique preserves sharp boundaries in the image while preventing the formation of staircase artifacts in the regions of smoothly varying pixel intensities. It also shows reduced error measures compared with second-order nonlinear diffusion reconstruction or TV and converges faster than TV-based methods. Conclusion Because nonlinear diffusion is known to be an effective alternative to TV for edge-preserving reconstruction, the crucial aspect of staircase artifact removal is addressed. Reconstruction is found to be stable for the experimentally determined range of fourth-order regularization parameter, and therefore not does not introduce a parameter search. Hence, the computational simplicity of second-order diffusion is retained.