Motivation: MRI reconstruction via direct pseudoinversion of the encoding matrix (Pinv-Recon) is not widely used due to its assumed computational infeasibility compared to FFT-based or iterative methods. However, novel MRI applications with small to medium matrix sizes could benefit from its ease of implementation and flexibility in handling various encoding mechanisms and distortions. Goal(s): Demonstrate the applicability of Pinv-Recon in novel settings. Approach: Pinv-Recon was validated on various dataset sizes, including hyperpolarized Xenon-129, hyperpolarized Carbon-13 and proton datasets, with performance comparisons to conventional methods. Results: By bypassing FFT, Pinv-Recon eliminates gridding artifacts in non-Cartesian datasets, improves B0 correction and simplifies non-Cartesian SENSE reconstruction. Impact: Highlighting the application of generalized MR image reconstruction via direct pseudoinversion of the encoding matrix (Pinv-Recon) to hyperpolarized MRI and emphasizing its feasibility with modern computational infrastructure, ease of implementation, and advantages over conventional FFT-based approaches.