C. Future directions

As our results demonstrate, the SCAD regularization allows for more accurate reconstructions from highly undersampled data and hence reduced sampling rate for rapid data acquisitions. However, it is worth to mention the limitations and future outlook of the proposed SCAD-ADMM algorithm. In this study, we evaluated the proposed algorithm for Cartesian approximation of radial and spiral trajectories and compared its performance with l1-based ADMM. This approximation and synthetization of the k-spaces from magnitude images cannot accurately represent the actual data acquisition process in MRI. Nevertheless, our comparative results showed that the proposed regularization can improve the performance of l1-based regularization using adaptive identification and preservation of image features. Future work will focus on the evaluation of the proposed

104 regularization for non-Cartesian datasets and also parallel MR image reconstruction using AL methods [40].

Performance assessment of the SCAD norm in comparison with a family of reweighted l1 norms and l0

homotopic norms within the presented AL framework is also underway.

V. Conclusion

In this study, we proposed a new regularization technique for compressed sensing MRI through the linearization of the non-convex SCAD potential function in the framework of augmented Lagrangian methods. Using variable splitting technique, the CS-MRI problem was formulated as a constrained optimization problem and solved efficiently in the AL framework. We exploited discrete gradients and wavelet transforms as a sparsifying transform and demonstrated that the linearized SCAD regularization is an iteratively weighted l1 regularization with improved edge-preserving and sparsity-promoting properties. The performance of the algorithm was evaluated using phantom simulations and retrospective CS-MRI of clinical studies. It was found that the proposed regularization technique outperforms the conventional l1 regularization and can find applications in CS-MRI image reconstruction.

Acknowledgment

This work was supported by the Swiss National Science Foundation under grant SNSF 31003A-135576 and the Indo-Swiss Joint Research Programme ISJRP 138866.

105

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Chapter 7

Magnetic resonance imaging-guided attenuation