Computational Feasibility of MR Image Reconstruction via Explicit Construction and Inversion of the Encoding Matrix

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.