Efficient MRI Reconstruction Through Singular Value Decomposition

Abstract

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Magnetic Resonance Imaging (MRI) data exhibit strong spatial correlations, making them well suited for compression and denoising using low-rank approximations. Singular Value Decomposition (SVD), a robust matrix factorization technique, enables efficient representation of such data by decomposing an image into orthogonal spatial and temporal components and preserving only the most significant singular values. In this study, we apply a slice-wise low-rank SVD-based reconstruction method to a 3D MRI volume from an ischemic stroke dataset in NIfTI format. Each axial slice is decomposed using SVD, and a low-rank approximation is performed by retaining the top 50 singular values, effectively reducing noise and artifacts while maintaining essential structural information. The reconstructed volume is then qualitatively compared to the original through visual inspection and quantitatively evaluated using standard image quality metrics-Mean Squared Error (MSE), Peak Signal-to-Noise Ratio (PSNR), and Structural Similarity Index Measure (SSIM). Results demonstrate that the proposed low-rank SVD reconstruction improves image clarity and fidelity, particularly in the context of compressed sensing MRI, highlighting its potential for efficient and artifact-suppressing reconstruction in clinical and research applications.