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.