dMRI reconstruction based on tensor ring and ℓ1 − 2 norm constrained model with Plug-and-Play regularization

Abstract

Compressed sensing(CS) has been identified to significantly accelerate magnetic resonance imaging from the highly under-sampled k-space data. In this paper, based on low-rank plus sparse (L plus S) decomposition model, we propose a new dynamic MRI(dMRI) reconstruction model by introducing the tensor-ring(TR) rank and ℓ_{1 − 2} norm constrained framework with an embedded Plug-and-Play(PnP) based regularization(TRLP). More precisely, first, in order to exploit the low-rank and sparse properties in dMRI more sufficiently, the L plus S model is utilized to decompose dMRI into two components, low-rank and sparse. Second, considering that the low-rank property of dMRI is mainly presented inside each frame, and the temporal correlation is not very strong, the TR-rank is employed to constrain the low-rank prior instead of tensor tubal rank. And comparing to mode-n rank, TR-rank can exploit the low-rank prior brought by dMRI due to different structures in the image from higher dimensions in more flexible manner. Third, using ℓ_{1 − 2} norm to constrain sparse prior can approximate ℓ₀ norm better than ℓ₁ norm, leading to promoting sparsity of sparse component. Finally, since low-rank component lacks the ability of removing noise with low-rank property, we employ an implicit PnP-based regularization to break through this limitation and preserve more image details. Extensive experimental results suggest that the proposed method achieves superior performance over compared methods in terms of quantitative evaluation and visual inspection.