Magnetic Resonance Imaging via Weighted \(\ell _{1-p}\) Minimization

In Magnetic Resonance Imaging (MRI), reduction in scanning time and high reconstruction quality are of paramount value. The recent sparsity based optimization techniques offer a way out to this end. The weighted norm minimization in Compressed Sensing (CS) has become popular due to its capability in providing adaptive sparse solutions. The \(\ell _{1-p}\) , \(p>1\) , minimization on the other hand has recently gained attention of researchers due to its superiority in dealing with highly coherent matrices. Intending to exploit the best of both, we propose a weighed \(\ell _{1-p}\) minimization problem for \(p>1\) . While presenting its solver, we demonstrate that the proposed optimization problem reconstructs an MR image faithfully from a small set of its Fourier samples. We compare and contract our method with its existing counterparts that use CS based ideas.