Sparse Reconstruction Using the Integrated Approach for Magnetic Resonance Imaging

In order to decrease the number of data sampling and scan time in magnetic resonance imaging, a sparse reconstruction approach is proposed in this chapter. Integrating the conjugate gradient and orthogonal projection with line search, the proposed approach can solve both the convex problem and the nonconvex problem in the image reconstruction. Two imaging examples are illustrated in this chapter. Experimental results show that the better quality can be obtained when the proposed approach is used for nonconvex reconstruction than convex reconstruction. The proposed approach can effectively solve the optimization problem for sparse imaging; thus the magnetic resonance images can be reconstructed under highly under-sampled rate.