ALMA: a mathematics-driven approach for determining tuning parameters in generalized LASSO problems, with applications to MRI

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.

Free-running SIMilarity-Based Angiography (SIMBA) for simplified anatomical MR imaging of the heart

Purpose: Whole-heart MRA techniques typically target pre-determined motion states and address cardiac and respiratory dynamics independently. We propose a novel fast reconstruction algorithm, applicable to ungated free-running sequences, that leverages inherent similarities in the acquired data to avoid such physiological constraints. Theory and Methods: The proposed SIMilarity-Based Angiography (SIMBA) method clusters the continuously acquired k-space data in order to find a motion-consistent subset that can be reconstructed into a motion-suppressed whole-heart MRA. Free-running 3D radial datasets from six ferumoxytol-enhanced scans of pediatric cardiac patients and twelve non-contrast scans of healthy volunteers were reconstructed with a non-motion-suppressed regridding of all the acquired data (All Data), our proposed SIMBA method, and a previously published free-running framework (FRF) that uses cardiac and respiratory self-gating and compressed sensing. Images were compared for blood-myocardium interface sharpness, contrast ratio, and visibility of coronary artery ostia. Results: Both the fast SIMBA reconstruction (~20s) and the FRF provided significantly higher blood-myocardium sharpness than All Data (P<0.001). No significant difference was observed among the former two. Significantly higher blood-myocardium contrast ratio was obtained with SIMBA compared to All Data and FRF (P<0.01). More coronary ostia could be visualized with both SIMBA and FRF than with All Data (All Data: 4/36, SIMBA: 30/36, FRF: 33/36, both P<0.001) but no significant difference was found between the first two. Conclusion: The combination of free-running sequences and the fast SIMBA reconstruction, which operates without a priori assumptions related to physiological motion, forms a simple workflow for obtaining whole-heart MRA with sharp anatomical structures.