# LORAKI: Autocalibrated Recurrent Neural Networks for Autoregressive MRI Reconstruction in k-Space

arXiv: https://arxiv.org/abs/1904.09390 · HTML: https://mlsanity.com/paper/1904.09390/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Apr 2019.

## Built on by (most cited first, 28 of 28)

- [Unsupervised MRI Reconstruction via Zero-Shot Learned Adversarial Transformers](https://mlsanity.com/paper/2105.08059/) (2021)
- [Multi-Modal Transformer for Accelerated MR Imaging](https://mlsanity.com/paper/2106.14248/) (2021)
- [Recurrent Variational Network: A Deep Learning Inverse Problem Solver applied to the task of Accelerated MRI Reconstruction](https://mlsanity.com/paper/2111.09639/) (2021)
- [Self-Score: Self-Supervised Learning on Score-Based Models for MRI Reconstruction](https://mlsanity.com/paper/2209.00835/) (2022)
- [A review and experimental evaluation of deep learning methods for MRI reconstruction](https://mlsanity.com/paper/2109.08618/) (2021)
- [One-shot Generative Prior in Hankel-k-space for Parallel Imaging Reconstruction](https://mlsanity.com/paper/2208.07181/) (2022)
- [On Retrospective k-space Subsampling schemes For Deep MRI Reconstruction](https://mlsanity.com/paper/2301.08365/) (2023)
- [SPIRiT-Diffusion: Self-Consistency Driven Diffusion Model for Accelerated MRI](https://mlsanity.com/paper/2304.05060/) (2023)
- [WKGM: Weight-K-space Generative Model for Parallel Imaging Reconstruction](https://mlsanity.com/paper/2205.03883/) (2022)
- [Global k-Space Interpolation for Dynamic MRI Reconstruction using Masked Image Modeling](https://mlsanity.com/paper/2307.12672/) (2023)
- [Classification, Regression and Segmentation directly from k-Space in Cardiac MRI](https://mlsanity.com/paper/2407.20108/) (2024)
- [Physics-Driven Autoregressive State Space Models for Medical Image Reconstruction](https://mlsanity.com/paper/2412.09331/) (2024)
- [Equilibrated Zeroth-Order Unrolled Deep Networks for Accelerated MRI](https://mlsanity.com/paper/2112.09891/) (2021)
- [K-space and Image Domain Collaborative Energy based Model for Parallel MRI Reconstruction](https://mlsanity.com/paper/2203.10776/) (2022)
- [Robust Physics-based Deep MRI Reconstruction Via Diffusion Purification](https://mlsanity.com/paper/2309.05794/) (2023)
- [Matrix Completion-Informed Deep Unfolded Equilibrium Models for Self-Supervised k-Space Interpolation in MRI](https://mlsanity.com/paper/2309.13571/) (2023)
- [Score-based Diffusion Models With Self-supervised Learning For Accelerated 3D Multi-contrast Cardiac Magnetic Resonance Imaging](https://mlsanity.com/paper/2310.04669/) (2023)
- [Assessment of Data Consistency through Cascades of Independently Recurrent Inference Machines for fast and robust accelerated MRI reconstruction](https://mlsanity.com/paper/2111.15498/) (2021)
- [CAMP-Net: Consistency-Aware Multi-Prior Network for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2306.11238/) (2023)
- [A scan-specific unsupervised method for parallel MRI reconstruction via implicit neural representation](https://mlsanity.com/paper/2210.10439/) (2022)
- [Complex Network for Complex Problems: A comparative study of CNN and Complex-valued CNN](https://mlsanity.com/paper/2302.04584/) (2023)
- [Adaptive Local Neighborhood-based Neural Networks for MR Image Reconstruction from Undersampled Data](https://mlsanity.com/paper/2206.00775/) (2022)
- [Re-Visible Dual-Domain Self-Supervised Deep Unfolding Network for MRI Reconstruction](https://mlsanity.com/paper/2501.03737/) (2025)
- [Virtual Coil Augmentation Technology for MR Coil Extrapolation via Deep Learning](https://mlsanity.com/paper/2201.07540/) (2022)
- [Wave-Encoded Model-based Deep Learning for Highly Accelerated Imaging with Joint Reconstruction](https://mlsanity.com/paper/2202.02814/) (2022)
- [ERNAS: An Evolutionary Neural Architecture Search for Magnetic Resonance Image Reconstructions](https://mlsanity.com/paper/2206.07280/) (2022)
- [Towards Globally Predictable k-Space Interpolation: A White-box Transformer Approach](https://mlsanity.com/paper/2508.04051/) (2025)
- [Beyond Training from Scratch: Foundation Models for Data-Efficient and Generalizable Cardiac MRI Reconstruction](https://mlsanity.com/paper/2610.08109/) (2026)

## Abstract (arXiv)

We propose and evaluate a new MRI reconstruction method named LORAKI that trains an autocalibrated scan-specific recurrent neural network (RNN) to recover missing k-space data. Methods like GRAPPA, SPIRiT, and AC-LORAKS assume that k-space data has shift-invariant autoregressive structure, and that the scan-specific autoregression relationships needed to recover missing samples can be learned from fully-sampled autocalibration (ACS) data. Recently, the structure of the linear GRAPPA method has been translated into a nonlinear deep learning method named RAKI. RAKI uses ACS data to train an artificial neural network to interpolate missing k-space samples, and often outperforms GRAPPA. In this work, we apply a similar principle to translate the linear AC-LORAKS method (simultaneously incorporating support, phase, and parallel imaging constraints) into a nonlinear deep learning method named LORAKI. Since AC-LORAKS is iterative and convolutional, LORAKI takes the form of a convolutional RNN. This new architecture admits a wide range of sampling patterns, and even calibrationless patterns are possible if synthetic ACS data is generated. The performance of LORAKI was evaluated with retrospectively undersampled brain datasets, with comparisons against other related reconstruction methods. Results suggest that LORAKI can provide improved reconstruction compared to other scan-specific autocalibrated reconstruction methods like GRAPPA, RAKI, and AC-LORAKS. LORAKI offers a new deep-learning approach to MRI reconstruction based on RNNs in k-space, and enables improved image quality and enhanced sampling flexibility.