Constrained Higher Degree Total p-Variation Minimization for MRI Reconstruction From Undersampled K-Space Data

Background: In Magnetic Resonance (MR) image reconstruction, Higher Degree Total Variation (HDTV) using high-order directional derivatives outperforms total variation-based method in preserving edge information and suppressing unfavourable staircase artifacts. Traditional HDTV regularization, however, takes the form of L1-based, which is not the most straightforward way to maximize sparsity prior. Previous work has shown that nonconvex Lp-norm is potentially more effective than L1-norm in promoting sparsity. Methods: This work develops a Higher Degree Total p-variation (HDTpV) regularization model to enhance the sparsity utilization of HDTV and offers more accurate solutions for MR image reconstruction issues. To resolve the nonconvex optimization issue of the HDTpV minimization model, Split Bregman (SB) method was adopted to translate the original constrained problem into a succession of unconstrained subproblems, which can be solved by fast Fourier transform and generalized pshrinkage mapping. The qualitative and quantitative simulation experiments are conducted to demonstrate the accuracy and efficiency of the proposed method. Results & Conclusion: On the whole, improved performance is exhibited by the proposed method over the original HDTV-based method while applied to compressed MR image reconstruction.