Unsupervised Dynamic MRI Reconstruction via Low-Rank Patch-Based Tensor Functions with Implicit Neural Representation

Dynamic MRI suffers from limited spatiotemporal resolution due to long acquisition times. Undersam pling k-space can accelerate imaging, but it poses a major challenge for accurate image reconstruction. Supervised deep learning methods achieve impressive results, yet they rely on large fully sampled datasets which are often difficult to obtain. Recently, implicit neural representations (INR) have emerged as a powerful unsupervised paradigm that reconstructs images from a single undersampled dataset without external training data. However, existing INR-based methods still face challenges when applied to highly under sampled dynamic MRI, mainly due to their inefficient representation capacity and high computational cost. To address these issues, we propose TenF-INR, a novel unsupervised framework that integrates low-rank tensor modeling with INR, where each factor matrix in the tensor decomposition is modeled as a learnable factor function. Specifically, we employ INR to model learnable tensor functions within a low-rank decomposition, reducing the parameter space and computational burden. A patch-based nonlocal tensor modeling strategy further exploits temporal correlations and inter-patch similarities, enhancing the recovery of fine spatiotemporal details. Experiments on dynamic cardiac and abdominal datasets demonstrate that TenF INR achieves up to 21-fold acceleration, outperforming both supervised and unsupervised state-of-the-art methods in image quality, temporal fidelity, and quantitative accuracy. This work establishes an unsupervised learning framework for high-dimensional dynamic MRI reconstruction, offering a promising direction for efficient and interpretable modeling in advanced medical imaging applications.