提出高效算法提升压缩感知MRI重建质量并保证理论收敛
A Convergent Generalized Krylov Subspace Method for Compressed Sensing MRI Reconstruction with Gradient-Driven Denoisers
- 用广义克雷洛夫子空间法加速非凸优化求解
- 在螺旋与径向采集数据上验证了算法高效且结果准确
- 适合从事医学图像重建与优化算法研究者参考
基于模型的压缩感知（CS）MRI重建通过引入有效的图像正则项显著提升了重建质量。插件式和通过去噪正则化框架利用先进去噪器（如基于卷积神经网络的去噪器）取得了良好的实验性能，但其理论保障有限，因实际CNN常违反关键假设。相比之下，梯度驱动型去噪器表现相当，且满足理论分析所需条件更易。然而，求解相关优化问题仍计算成本高。为此，本文提出广义克雷洛夫子空间方法（GKSM），以高效求解该优化问题，并在非凸设置下建立了严格的收敛性保证。在螺旋和径向采样下的数值实验验证了GKSM的计算效率及理论预测的准确性。所提优化方法适用于任意线性逆问题。
原文摘要 · Abstract (English)
Model-based reconstruction plays a key role in compressed sensing (CS) MRI, as it incorporates effective image regularizers to improve the quality of reconstruction. The Plug-and-Play and Regularization-by-Denoising frameworks leverage advanced denoisers (e.g., convolutional neural network (CNN)-based denoisers) and have demonstrated strong empirical performance. However, their theoretical guarantees remain limited, as practical CNNs often violate key assumptions. In contrast, gradient-driven denoisers achieve competitive performance, and the required assumptions for theoretical analysis are easily satisfied. However, solving the associated optimization problem remains computationally demanding. To address this challenge, we propose a generalized Krylov subspace method (GKSM) to solve the optimization problem efficiently. Moreover, we also establish rigorous convergence guarantees for GKSM in nonconvex settings. Numerical experiments on CS MRI reconstruction with spiral and radial acquisitions validate both the computational efficiency of GKSM and the accuracy of the theoretical predictions. The proposed optimization method is applicable to any linear inverse problem.
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