# Image Reconstruction with Low-rankness and Self-consistency of k-space Data in Parallel MRI

arXiv: https://arxiv.org/abs/1909.02846 · HTML: https://mlsanity.com/paper/1909.02846/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Sep 2019.

## Built on by (most cited first, 13 of 13)

- [Unsupervised MRI Reconstruction via Zero-Shot Learned Adversarial Transformers](https://mlsanity.com/paper/2105.08059/) (2021)
- [One-dimensional Deep Low-rank and Sparse Network for Accelerated MRI](https://mlsanity.com/paper/2112.04721/) (2021)
- [IMJENSE: Scan-specific Implicit Representation for Joint Coil Sensitivity and Image Estimation in Parallel MRI](https://mlsanity.com/paper/2311.12892/) (2023)
- [Learning Fourier-Constrained Diffusion Bridges for MRI Reconstruction](https://mlsanity.com/paper/2308.01096/) (2023)
- [One-shot Generative Prior in Hankel-k-space for Parallel Imaging Reconstruction](https://mlsanity.com/paper/2208.07181/) (2022)
- [A Faithful Deep Sensitivity Estimation for Accelerated Magnetic Resonance Imaging](https://mlsanity.com/paper/2210.12723/) (2022)
- [DP-MDM: Detail-Preserving MR Reconstruction via Multiple Diffusion Models](https://mlsanity.com/paper/2405.05763/) (2024)
- [Bayesian Uncertainty-Aware MRI Reconstruction](https://mlsanity.com/paper/2603.13439/) (2026)
- [MCU-Net: A Multi-prior Collaborative Deep Unfolding Network with Gates-controlled Spatial Attention for Accelerated MR Image Reconstruction](https://mlsanity.com/paper/2402.03383/) (2024)
- [Low-rank Tensor Assisted K-space Generative Model for Parallel Imaging Reconstruction](https://mlsanity.com/paper/2212.05503/) (2022)
- [A Dynamics Theory of Implicit Regularization in Deep Low-Rank Matrix Factorization](https://mlsanity.com/paper/2212.14150/) (2022)
- [Trustworthy MRI Reconstruction via Bayesian Uncertainty Quantification with Sparsity Prior Models](https://mlsanity.com/paper/2606.17343/) (2026)
- [Stochastic Finite-Transition Learning and Exploration for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2610.13095/) (2026)

## Abstract (arXiv)

Parallel magnetic resonance imaging has served as an effective and widely adopted technique for accelerating scans. The advent of sparse sampling offers aggressive acceleration, allowing flexible sampling and better reconstruction. Nevertheless, faithfully reconstructing the image from limited data still poses a challenging task. Recent low-rank reconstruction methods exhibit superiority in providing a high-quality image. However, none of them employ the routinely acquired calibration data for improving image quality in parallel magnetic resonance imaging. In this work, an image reconstruction approach named STDLR-SPIRiT was proposed to explore the simultaneous two-directional low-rankness (STDLR) in the k-space data and to mine the data correlation from multiple receiver coils with the iterative self-consistent parallel imaging reconstruction (SPIRiT). The reconstruction problem was then solved with a singular value decomposition-free numerical algorithm. Experimental results of phantom and brain imaging data show that the proposed method outperforms the state-of-the-art methods in terms of suppressing artifacts and achieving the lowest error. Moreover, the proposed method exhibits robust reconstruction even when the auto-calibration signals are limited in parallel imaging. Overall the proposed method can be exploited to achieve better image quality for accelerated parallel magnetic resonance imaging.