Under-determined non-cartesian MR reconstruction with non-convex sparsity promoting analysis prior

1 notation:

1.1 Synthesis prior formulation

1.2 analysis prior formulation

2 main results :

2.1 In this paper, the authors present an optimization algorithms for non-convex problem. They use Lp norm to promote sparsity, of cause. The optimization algorithms are based on majorization minimization.

2.2 They claimed that the analysis prior formulation with redundant wavelet transform gives better reconstruction quality than the systhesis prior formulation with orthogonal wavelet transform.

redundant systhesis worse than orthogonal synthesis worse than redundant analysis.

my question : what about analysis synthesis and compared to l1 norm ? (in the paper they use l_0.8 norm)

The paper reminds me of the paper Image reconstruction from few-views by non-convex optimization. In this paper, authors use a TpV norm, which is the lp norm of total variation.

The optimization method is not proved to be convergence. but also the results show the lp norm leads to better reconstruction quality.