Correlation-Weighted Sparse Representation for Robust Liver DCE-MRI Decomposition Registration

Conducting an accurate motion correction of liver dynamic contrast-enhanced magnetic resonance (DCE-MR) imaging remains challenging because of intensity variations caused by contrast agents. Such variations lead to the failure of the traditional intensity-based registration method. To address this problem, we propose a correlation-weighted sparse representation framework to separate the contrast agent from original liver DCE-MR images. This framework allows the robust registration of motion components over time without intensity variances. Existing sparse coding techniques recover a 3D image containing only contrast agents (named contrast enhancement component) from a manually labeled dictionary, whose column has the same size with the original 3D volume (3D-t mode). The high dimension of the recovery target (3D volume) and the indistinguishability between the unenhanced and enhanced images make accurate coding difficult. In this paper, we predefine an ideal time-intensity curve containing only contrast agents (named contrast agent curve) and recover it from the transpose dictionary (t-3D mode), whose column has been updated into the original time-intensity curves. The low dimension of the target (1D curve) and the significant intergroup difference between contrast agent curves and non-contrast agent curves can estimate a series of pure contrast agent curves. A "correlation-weighted" constraint is introduced for the selection of a coding subset with more contrast agent curves, leading to an efficient and accurate sparse recovery process. Then, the contrast enhancement component can be estimated by the solved sparse coefficients' map and the ideal curve and subtracted from the original DCE-MRI. Finally, we register the de-enhanced images and apply the obtained deformation fields for the original DCE-MRI to achieve the goal of motion correction. We conduct the experiments on both simulated and real liver DCE-MRI data. Compared with other state-of-the-art DCE-MRI registration methods, the experimental results show that our method achieves a better registration performance with less computational efficiency.