MR Image Reconstruction via Sparse Representation: Modeling and Algorithm

To reduce acquisition time in magnetic resonance (MR) imaging, compressive sensing and sparse representation techniques have been developed to reconstruct MR images with partially acquired data. Although this has been a hot research topic in the field, it has not been used clinically due to three inherent problems of its current framework: potential loss of fine structures, difficulty to predefine model parameters, and long reconstruction time. The aim of this work is to tackle these problems. We propose to minimize the total variation of the underlying image, together with the `1 norm of the coefficients in its representation using a trained dictionary, as well as a fidelity term. Using a trained dictionary can take the advantage of prior knowledge and hence improve accuracy in reconstruction. Our data fidelity constraint is derived from the likelihood estimator of the recovering error in partial k-space to improve the robustness of the model to parameter selection. Moreover, a simple and efficient numerical scheme is provided to solve this model faster. The consequent experiments on both synthetic and in vivo data indicate the improvement of the proposed model in preserving fine structure, reducing computational cost, and flexibility of parameter decision.