4D-MRI Reconstruction of Thoracoabdominal Organs in Free Breathing Using Low-Rank and Sparse Matrix Decomposition

Purpose: The purpose was to present a method for four-dimensional magnetic resonance image (4D-MRI) reconstruction of thoracoabdominal organs from reduced data collection without increasing error by making use of a sparse model-based technique. Materials and Methods: In the proposed method, the number of encoded samples in k-space is reduced to save time; and a sparse model-based reconstruction technique called a low-rank plus sparse matrix decomposition (L+S) is applied to preserve image quality. Simulations were performed with encoded data reduced to one-third the full sampling amount. Image quality was compared between the ideal reconstructed image using the full sampling data, the reconstructed image using the conventional method (missing regions of k-space data filled by zeros), and the reconstructed image using the L+S technique. Results: In six subjects tested, the root mean square error between the ideal image and the L+S reconstructed image was within approximately 2% compared with a root mean square error of 3-4% for the undersampled images. Subjective visual inspection showed that the L+S technique provided similar image quality to the ideal images as well. Conclusion: The L+S technique was confirmed able to reduce artifacts and noise and provide image quality similar to that of the ideal image in one-third of the time needed for conventional acquisition.