outperforms the existing approaches.'
author:
- 'Jian-Feng Cai[^1]'
- 'Jae Kyu Choi[^2]'
- 'Ke Wei[^3]'
title: '[[Off-the-Grid Compressed Sensing MRI Reconstruction via Data Driven Tight Frame Regularization]{}]{}[^4]'
---

Magnetic resonance imaging, finite-rate-of-innovation, structured low rank matrix completion, (tight) wavelet frames, data driven tight frames, proximal alternating schemes

42B05, 65K15, 65R32, 68U10, 90C90, 92C55, 94A12, 94A20

Introduction {#Introduction}
============

Magnetic resonance imaging (MRI) is one of the most widely used medical imaging modality in clinical diagnosis [@E.M.Haacke1999]. It is non-radioactive, non-invasive, and has excellent soft tissue contrasts such as T1 and T2 with high spatial resolution [@Y.Liu2015]. Among these merits, the availability of high spatial resolution images, which will be the focus of this paper, facilitates early diagnosis by enabling the detection and characterization of clinically important lesions [@G.Ongie2015; @E.VanReeth2012]. However, since the so-called k-space data acquisition is limited due to physical (gradient amplitude and slew-rate) and physiological (nerve stimulation) constraints [@C.M.Hyun2018; @Y.Liu2015; @M.Lustig2007], there has been increasing demand for methods which can reduce the amount of acquired data without degrading the image quality [@M.Lustig2007].

When the k-space data is undersampled, the Nyquist sampling criterion is violated, and this inevitably leads to the aliasing in the reconstructed image [@M.Lustig2007]. In the 