Computational Feasibility of MR Image Reconstruction via Explicit Construction and Inversion of the Encoding Matrix
Kylie Yeung, Fergus Vincent Gleeson, Rolf F. Schulte, Damian J. Tyler, James T. Grist, Florian Wiesinger · Proceedings on CD-ROM - International Society for Magnetic Resonance in Medicine. Scientific Meeting and Exhibition/Proceedings of the International Society for Magnetic Resonance in Medicine, Scientific Meeting and Exhibition · 2025
Motivation: MR reconstruction using the direct pseudoinverse of the encoding matrix, which is a simple and versatile approach, has not been widely adopted clinically due to its perceived computational intractability. Goal(s): To demonstrate the computational feasibility of generalized MR image reconstruction via direct pseudoinversion of the encoding matrix using high-end computational systems similar to modern MR reconstruction computers. Approach: To test computational times required for direct pseudoinversion of various encoding matrices and for calculating relevant image metrics. Results: SVD computation time scales with the ~1.4th power of the cardinality of the encoding matrix. Spatial-response-functions and noise matrices were also derived. Impact: Demonstration of the current computational feasibility of generalized MR image reconstruction via direct pseudoinversion of the encoding matrix (Pinv-Recon), which is as a simple and versatile reconstruction approach able to incorporate a variety of encoding mechanisms and distortions.