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.

通过 TV-regularized LASSO 方法和 ALMA 算法，本研究为 MRI 重建过程中选择合适的调优参数提供了一种数值求解约束优化问题的有效工具。