Learning-based Optimization of the Under-sampling Pattern in MRI (1901.01960v2)

Abstract: Acquisition of Magnetic Resonance Imaging (MRI) scans can be accelerated by under-sampling in k-space (i.e., the Fourier domain). In this paper, we consider the problem of optimizing the sub-sampling pattern in a data-driven fashion. Since the reconstruction model's performance depends on the sub-sampling pattern, we combine the two problems. For a given sparsity constraint, our method optimizes the sub-sampling pattern and reconstruction model, using an end-to-end learning strategy. Our algorithm learns from full-resolution data that are under-sampled retrospectively, yielding a sub-sampling pattern and reconstruction model that are customized to the type of images represented in the training data. The proposed method, which we call LOUPE (Learning-based Optimization of the Under-sampling PattErn), was implemented by modifying a U-Net, a widely-used convolutional neural network architecture, that we append with the forward model that encodes the under-sampling process. Our experiments with T1-weighted structural brain MRI scans show that the optimized sub-sampling pattern can yield significantly more accurate reconstructions compared to standard random uniform, variable density or equispaced under-sampling schemes. The code is made available at: https://github.com/cagladbahadir/LOUPE .

• The paper introduces LOUPE, a method that jointly optimizes under-sampling patterns and MRI reconstruction using a convolutional neural network.
• It integrates a U-Net based forward model with stochastic gradient descent and Monte Carlo sampling to tailor k-space acquisition.
• Empirical results on T1-weighted brain MRI show a 10% efficiency gain over traditional schemes, indicating strong potential for clinical acceleration.

Learning-based Optimization of Under-sampling Patterns in MRI

The paper under discussion presents a robust framework for optimizing the under-sampling patterns in Magnetic Resonance Imaging (MRI) using a learning-based approach named LOUPE (Learning-based Optimization of the Under-sampling PattErn), which efficiently integrates sub-sampling pattern optimization with MRI reconstruction using a convolutional neural network architecture. This synergy not only enhances the image reconstruction but also strategically selects the under-sampling pattern to achieve higher image fidelity under compressed sensing regimes.

MRI is inherently time-consuming due to the requirement to fully sample k-space, which corresponds to the spatial frequency domain of the imaging data. Compressed sensing has emerged as a pivotal technique for mitigating the lengthy acquisition times in MRI, allowing for under-sampling without hardware augmentation. However, optimizing under-sampling patterns that closely cater to the reconstruction model's specific requirements remains a challenging yet critical element.

Methodology Overview

LOUPE extends the pioneering use of U-Net architecture by incorporating the forward model to encode the under-sampling process as part of an end-to-end learning system. Given full-resolution data, LOUPE performs retrospective under-sampling to derive both the optimized sub-sampling pattern and a reconstruction model tailored to the data. The objective function, as formulated in the paper, juxtaposes a sparsity criterion against the reconstruction fidelity, striving to maintain image quality despite aggressive under-sampling.

The optimization problem is solved through stochastic gradient descent methods, leveraging the differentiable nature of deep learning models to modify the sub-sampling patterns effectively. LOUPE employs a Monte Carlo strategy to sample k-space, observing the transformations on reconstruction quality and allowing rapid assessment and pivoting during model training.

Empirical Findings and Challenges

Empirical evaluations were carried out using T1-weighted structural brain MRI scans, benchmarked against traditional under-sampling schemes (random uniform, variable density, and equispaced Cartesian sampling). Results unequivocally indicated that LOUPE's optimized pattern markedly enhanced reconstruction accuracy across various conditions. The optimized mask demonstrated a 10% sub-sampling efficiency without calibration regions, which outperformed conventional variable density masks in high-frequency k-space areas.

Amongst the reconstruction methods tested—including ALOHA and BM3D—the deep learning models, specifically those integrated within LOUPE, manifested superior computational efficiency. This efficiency is attributable to non-iterative forward passes through the reconstruction network, circumventing the computational load of traditional iterative regression approaches.

Implications and Future Directions

LOUPE presents a significant advancement in compressed sensing MRI, especially in clinical contexts where acquisition speed directly translates to reduced operational costs and improved patient throughput. The framework's adaptability to different imaging sequences and organ domains provides broad applicability across MRI modalities.

Future developments could focus on refining sparsity metrics in line with hardware constraints or tailoring the reconstruction loss to better capture anatomical details and even pathology. Integrating parallel imaging techniques could further augment acceleration capabilities, while exploring optimization for multi-dimensional sub-sampling grids promises novel avenues for precise medical image reconstruction.

The availability of LOUPE's codebase at GitHub invites further exploration, collaboration, and validation across diverse datasets, fostering a community-led evolution of MRI acquisition and reconstruction techniques. As the intersection of deep learning and medical imaging deepens, methodologies like LOUPE hold potential not just for MRI but for wider applications where signal undersampling meets reconstruction fidelity challenges. Such endeavors actively contribute to the accelerated development of AI-driven solutions in healthcare imaging.