Discrete Shearlets as a Sparsifying Transform in Low-Rank Plus Sparse Decomposition for Undersampled (k, t)-Space MR Data.

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Protonotarios, Nicholas E  ORCID logo  https://orcid.org/0000-0002-7701-5644
Tzampazidou, Evangelia  ORCID logo  https://orcid.org/0000-0003-2193-231X

The discrete shearlet transformation accurately represents the discontinuities and edges occurring in magnetic resonance imaging, providing an excellent option of a sparsifying transform. In the present paper, we examine the use of discrete shearlets over other sparsifying transforms in a low-rank plus sparse decomposition problem, denoted by L+S. The proposed algorithm is evaluated on simulated dynamic contrast enhanced (DCE) and small bowel data. For the small bowel, eight subjects were scanned; the sequence was run first on breath-holding and subsequently on free-breathing, without changing the anatomical position of the subject. The reconstruction performance of the proposed algorithm was evaluated against k-t FOCUSS. L+S decomposition, using discrete shearlets as sparsifying transforms, successfully separated the low-rank (background and periodic motion) from the sparse component (enhancement or bowel motility) for both DCE and small bowel data. Motion estimated from low-rank of DCE data is closer to ground truth deformations than motion estimated from L and S. Motility metrics derived from the S component of free-breathing data were not significantly different from the ones from breath-holding data up to four-fold undersampling, indicating that bowel (rapid/random) motility is isolated in S. Our work strongly supports the use of discrete shearlets as a sparsifying transform in a L+S decomposition for undersampled MR data.

MRI, discrete shearlet transform, dynamic contrast enhanced (DCE), image reconstruction, low-rank plus sparse decomposition, robust principal component analysis (RPCA), small bowel imaging
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J Imaging
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