of an image [@J.F.Cai2014; @J.K.Choi2018; @J.Wang2015; @R.Zhan2016], to the best of our knowledge, this is the first work that applies this approach for the MRI restoration based on a continuous image model. Finally, the numerical experiments show that our data driven tight frame approach outperforms the structured low rank matrix approaches based on \[LRSMCompletion\], leading to the state-of-the-art performance.

The rest of this paper is organized as follows. We first briefly review the related concepts, including (data driven) tight frames and structured low rank matrix approaches for CS-MRI, in \[Preliminaries\]. Then we present the off-the-grid CS-MRI reconstruction approach based on data driven tight frames and the alternating minimization algorithm in \[ModelandAlgorithm\], followed by the convergence of the algorithm. In \[Experiments\], experimental results are reported to demonstrate the performance of our new CS-MRI restoration method, and \[Conclusion\] concludes this paper with a few future directions.

Preliminaries and related works {#Preliminaries}
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Introduction on tight frames {#TightFrames}
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Here we provide a brief introduction on tight wavelet frames and data driven tight frames. Interested readers may consult [@J.F.Cai2008; @B.Dong2013; @B.Dong2015; @A.Ron1997; @Shen2010] for details on tight wavelet frames, and [@C.Bao2015; @J.F.Cai2014] for details on data driven tight frames. For the sake of 