Joint reconstruction of low-rank and sparse components from undersampled (k, t)-space small bowel data

Quantification of small bowel motility is a potential marker of disorders and assessment of response to therapy. MR imaging is a non-invasive diagnostic tool that can depict small bowel motion. Adequate temporal resolution and coverage is important for accurate estimation of small bowel motility. Compressed sensing exploits the expected sparsity in a transform domain and can reconstruct randomly undersampled k-space data, thus significantly accelerating the MR acquisition. A non linear reconstruction is required to promote the sparsity while maintaining the consistency with the acquired data. An alternative sparse domain is the singular values of a matrix and this can be promoted using low rank. In this work an adaptation of the split Bregman reconstruction is used to recover low rank and sparse components from simulated undersampled dynamic 3D data. Simulated small bowel datasets are generated for different undersampling factors of 4 and 8. The proposed method improved the correspondence to the scanner-reconstructed image compared to the zero filled FFT, which could allow us to improve the temporal resolution of the scan. Motility metrics could be accurately recovered up to an undersampling factor of 4.