Deep-learning-based Optimization of the Under-sampling Pattern in MRI (1907.11374v3)

Abstract: In compressed sensing MRI (CS-MRI), k-space measurements are under-sampled to achieve accelerated scan times. CS-MRI presents two fundamental problems: (1) where to sample and (2) how to reconstruct an under-sampled scan. In this paper, we tackle both problems simultaneously for the specific case of 2D Cartesian sampling, using a novel end-to-end learning framework that we call LOUPE (Learning-based Optimization of the Under-sampling PattErn). Our method trains a neural network model on a set of full-resolution MRI scans, which are retrospectively under-sampled on a 2D Cartesian grid and forwarded to an anti-aliasing (a.k.a. reconstruction) model that computes a reconstruction, which is in turn compared with the input. This formulation enables a data-driven optimized under-sampling pattern at a given sparsity level. In our experiments, we demonstrate that LOUPE-optimized under-sampling masks are data-dependent, varying significantly with the imaged anatomy, and perform well with different reconstruction methods. We present empirical results obtained with a large-scale, publicly available knee MRI dataset, where LOUPE offered superior reconstruction quality across different conditions. Even with an aggressive 8-fold acceleration rate, LOUPE's reconstructions contained much of the anatomical detail that was missed by alternative masks and reconstruction methods. Our experiments also show how LOUPE yielded optimal under-sampling patterns that were significantly different for brain vs knee MRI scans. Our code is made freely available at https://github.com/cagladbahadir/LOUPE/.

• The paper presents LOUPE, a framework that uses deep learning to simultaneously optimize under-sampling patterns and image reconstruction in MRI.
• It achieves superior diagnostic quality at high acceleration rates by outperforming traditional methods with improved PSNR, SSIM, and HFEN metrics.
• A constrained variant adapts the optimized patterns for physical feasibility, ensuring compatibility with realistic MR scanning protocols.

Deep-Learning-Based Optimization of the Under-sampling Pattern in MRI

The paper "Deep-learning-based Optimization of the Under-sampling Pattern in MRI" presents a novel approach to improve compressed sensing MRI (CS-MRI) by simultaneously optimizing under-sampling patterns and image reconstruction algorithms using deep learning. The proposed method, Learning-based Optimization of the Under-sampling PattErn (LOUPE), introduces an innovative framework that utilizes neural networks to derive both optimal sampling patterns and reconstructions, advancing the diagnostic quality of MRI scans while significantly reducing acquisition time.

In CS-MRI, one of the fundamental challenges is balancing the trade-off between accelerated image acquisition, achieved through under-sampling in k-space, and maintaining high reconstruction fidelity. Conventionally, sampling patterns are chosen heuristically, often based on pre-defined strategies such as random uniform or variable density under-sampling, which may not be optimal for all anatomical regions or image modalities. The reconstruction problem, on the other hand, is typically approached with regularization-based optimization that uses prior knowledge, sometimes resulting in computationally intensive iterative algorithms.

LOUPE tackles these challenges by bridging the gap between sampling pattern design and reconstruction. By leveraging an end-to-end deep learning model, LOUPE optimizes under-sampling patterns in a data-driven manner. The framework comprises two main components: a probabilistic mask that governs the under-sampling pattern and a deep neural network for reconstruction. The probabilistic mask introduces a learnable Bernoulli distribution across the k-space grid, where each element's probability being sampled is adjusted during training to minimize reconstruction error.

The empirical evaluation of LOUPE, performed on the publicly available NYU fastMRI knee dataset, demonstrates its efficacy across different anatomical contexts. At high acceleration rates (e.g., 8-fold), LOUPE-derived sampling patterns excel in preserving anatomical details compared to traditional methods. Notably, experiments reveal a discrepancy in optimal sampling patterns between knee and brain MRI, which LOUPE adapts efficiently due to its data-driven nature. Comprehensive assessments using various reconstruction metrics—PSNR, SSIM, and HFEN—support these claims, with LOUPE consistently outperforming benchmark under-sampling configurations when combined with U-Net-based reconstructions.

The theoretical contribution of LOUPE lies in its framework that combines and optimizes sampling and reconstruction in MRI, a previously decoupled problem. The method effectively demonstrates significant improvements even when paired with non-deep learning reconstruction approaches, indicating its broad applicability.

One of the limitations addressed by the authors is the physical realizability of the optimized under-sampling patterns; the patterns need to be viable for MR systems. To overcome this, a constrained version of LOUPE is proposed, limiting patterns to feasible scan protocols such as line-based sampling, showing its adaptability to real-world scenarios.

Future directions for this research include refining the approximation methods used for the probabilistic mask during training, potentially enhancing fidelity and robustness. Further exploration into multi-coil imaging settings could provide another dimension of efficiency, given the synergy between hardware advancements and LOUPE's optimization framework. As MRI technology progresses, incorporating LOUPE into clinical applications could help mitigate costs and improve access, especially for time-sensitive and motion-prone examinations. The integration of advanced machine learning paradigms in the design of sampling strategies, as illustrated by this work, marks a significant stride toward more efficient and reliable MRI diagnostics.