L0-compressed sensing for parallel dynamic MRI using sparse Bayesian learning

Since the advent of compressed sensing in dynamic MR imaging area, a number of l₁-compressed sensing algorithms have been proposed to improve the resolution. Recently, it was shown that by solving an l_p minimization problem with 0 ≤ p <; 1, the number of required measurements for an exact sparse reconstruction is more reduced than in solving an l₁ minimization. However, when 0 ≤ p <; 1, the problem is not convex and there exist many local minima. To deal with this problem, we adopted an empirical Bayesian approach called sparse Bayesian learning (SBL). The main contribution of this paper is to extend the idea for parallel dynamic MR imaging problems. By exploiting the simultaneous sparsity, the algorithm outperforms other methods, especially when the coil sensitivity map is not accurate. Numerical results confirms the theory.