ALMA：一种基于数学的方法，用于确定广义LASSO问题中的调优参数，并应用于MRI
ALMA: a mathematics-driven approach for determining tuning parameters in generalized LASSO problems, with applications to MRI
AI总结：
针对MRI重建中TV-LASSO调优参数依赖手动选择的问题，提出基于数学的迭代算法ALMA，可自动计算广义LASSO调优参数，并适用于多种正则化及非笛卡尔采样，提升重建可靠性。
摘要：
磁共振成像（MRI）是一种强大的技术，用于对人体内部结构进行非侵入性在体可视化。稀疏性常被用于加速信号采集或克服运动伪影的影响，从而提高图像重建的质量。图像重建算法使用TV正则化LASSO（全变分正则化LASSO）来恢复欠采样信号中缺失的信息，通过清除数据中的噪声并优化稀疏性。调优参数调节着这两个方面之间的平衡；其选择影响重建的质量。目前，缺乏通用的确定性技术来选择这些参数，这些参数常常是手动选择的，从而妨碍了重建的可靠性。在此，我们提出了ALMA（拉格朗日乘数逼近算法），一种迭代的基于数学的技术，用于在MRI重建过程中计算广义LASSO问题的调优参数。我们通过体模上的TV-LASSO在MRI背景下定量分析了这些参数在图像重建中的性能。尽管我们的研究集中在TV-LASSO上，但这里开发的技术对广泛的应用具有重要前景。ALMA不仅适用于更广义的LASSO问题，而且能够稳健地适应除全变分之外的其他形式的正则化。此外，它还能有效处理非笛卡尔采样轨迹，从而拓宽了其在复杂数据重建场景中的实用性。更一般地，ALMA为跨学科解决约束优化问题提供了强大的工具，为先进的计算挑战提供了多功能且具有影响力的解决方案。
英文摘要：
Magnetic Resonance Imaging (MRI) is a powerful technique employed for non-invasive in vivo visualization of internal structures. Sparsity is often deployed to accelerate the signal acquisition or overcome the presence of motion artifacts, improving the quality of image reconstruction. Image reconstruction algorithms use TV-regularized LASSO (Total Variation-regularized LASSO) to retrieve the missing information of undersampled signals, by cleaning the data of noise and while optimizing sparsity. A tuning parameter moderates the balance between these two aspects; its choice affecting the quality of the reconstructions. Currently, there is a lack of general deterministic techniques to choose these parameters, which are oftentimes manually selected and thus hinder the reliability of the reconstructions. Here, we present ALMA (Algorithm for Lagrange Multipliers Approximation), an iterative mathematics-inspired technique that computes tuning parameters for generalized LASSO problems during MRI reconstruction. We analyze quantitatively the performance of these parameters for imaging reconstructions via TV-LASSO in an MRI context on phantoms. Although our study concentrates on TV-LASSO, the techniques developed here hold significant promise for a wide array of applications. ALMA is not only adaptable to more generalized LASSO problems but is also robust to accommodate other forms of regularization beyond total variation. Moreover, it extends effectively to handle non-Cartesian sampling trajectories, broadening its utility in complex data reconstruction scenarios. More generally, ALMA provides a powerful tool for numerically solving constrained optimization problems across various disciplines, offering a versatile and impactful solution for advanced computational challenges.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
