[Paper Review] LORAKI: Autocalibrated Recurrent Neural Networks for Autoregressive MRI Reconstruction in k-Space

Tae Hyung Kim, Pratyush Garg+1 more|arXiv (Cornell University)|Apr 20, 2019

Advanced MRI Techniques and Applications23 references44 citations

TL;DR

LORAKI trains a scan-specific autocalibrated convolutional RNN to interpolate missing k-space samples, showing improved reconstruction over GRAPPA, RAKI, and AC-LORAKS across tested sampling schemes.

ABSTRACT

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.

Motivation & Objective

• Motivate faster MRI by reconstructing undersampled k-space data using autocalibrated, scan-specific models.
• Introduce LORAKI, a nonlinear convolutional RNN that extends AC-LORAKS and RAKI principles.
• Leverage autocalibration data to learn scan-specific autoregressive relationships in k-space.
• Demonstrate that LORAKI can accommodate a wide range of sampling patterns, including synthetic ACS data.

Proposed method

• Formulate LORAKI as a two-layer convolutional RNN with nonlinear ReLU activations inside a Landweber-inspired iterative scheme.
• Represent k-space interpolation as a learned, nonlinear autoregressive process that uses ACS data for training.
• Use ellipsoidal convolution kernels to enforce isotropic, constrained reconstruction within a structured low-rank framework.
• Train the network with ACS data (and optionally synthetic ACS data derived from preliminary reconstructions).
• Handle complex-valued data by using real-valued channels and virtual conjugate coils to capture phase constraints.

Experimental results

Research questions

• RQ1 Can LORAKI improve reconstruction quality over GRAPPA, RAKI, and AC-LORAKS for various Cartesian undersampling patterns?
• RQ2 Does incorporating synthetic ACS data enhance performance when actual ACS data is limited?
• RQ3 Is LORAKI robust to different undersampling schemes (uniform, random, partial Fourier) while maintaining compatibility with AC-LORAKS constraints?

Key findings

• LORAKI yields improved reconstruction quality versus GRAPPA, RAKI, and AC-LORAKS in retrospective brain MRI undersampling tests.
• Using synthetic ACS data can match or surpass the benefit of original ACS data, particularly when original ACS is limited.
• LORAKI remains effective across multiple sampling patterns, including random and partial Fourier undersampling, with favorable error characteristics across spatial frequencies.
• In calibrationless scenarios, LORAKI with synthetic ACS data often outperforms calibrationless baselines when initial reconstructions can provide useful ACS guidance.