Algebraic methods and computational strategies for pseudoinverse-based MR image reconstruction (Pinv-Recon).

Area of Science:

• Medical Imaging
• Computational Science
• Linear Algebra

Background:

• Magnetic Resonance Imaging (MRI) reconstruction is a linear inverse problem.
• Historically, Fast Fourier Transforms (FFT) and iterative methods were preferred over pseudoinversion (Pinv-Recon) due to computational concerns.
• Modern hardware and software advancements necessitate revisiting Pinv-Recon.

Purpose of the Study:

• To re-evaluate the computational feasibility and versatility of Pinv-Recon in modern MRI.
• To compare different matrix inversion strategies and regularization effects within the Pinv-Recon framework.
• To integrate advanced encoding physics into a unified Pinv-Recon approach.

Main Methods:

• Reconstruction via explicit pseudoinversion of the encoding matrix (Pinv-Recon).
• Comparison of various matrix inversion techniques, including Singular Value Decomposition (SVD) and Cholesky decomposition.
• Assessment of regularization effects and incorporation of advanced encoding physics.

Main Results:

• Cholesky decomposition offers a two-order-of-magnitude improvement in computational efficiency over SVD-based methods.
• Pinv-Recon demonstrated versatility across diverse in vivo datasets, from low- to high-resolution imaging.
• The framework successfully incorporated advanced encoding physics.

Conclusions:

• Pinv-Recon is a computationally efficient and robust framework for MRI reconstruction.
• This revisited method supports the growing trend towards open-source and reproducible MRI research.
• Pinv-Recon is suitable for a wide range of MRI applications, including functional, metabolic, and high-resolution imaging.