Aug 2026· IEEE journal of biomedical and health informatics· Vol PP, pp. 1-14· 0 citations
Medicine
TL;DR
TenF-INR is proposed, 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 within a low-rank decomposition, reducing the parameter space and computational burden.
Abstract
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.
Modeling shared and subject-specific structure in multisubject spatiotemporal data remains challenging, particularly in neuroimaging, where both spatial and temporal patterns exhibit rich variability across subjects. Existing matrix and tensor decompositions provide interpretable factorizations, but rely on fixed multilinear structures or coupling schemes that may limit their flexibility in capturing complex variability. In this work, we introduce a spatiotemporal variational tensor decomposition (ST-VTD) framework that combines a tensor factorization generative model with structured priors to jointly represent spatial maps and temporal dynamics. Spatial factors are regularized to promote a low-rank structure inspired by the LL1 decomposition, while temporal factors are modeled using a learned Long short-term memory (LSTM)-based prior, enabling flexible and adaptive dynamics. Posterior inference is performed using an amortized variational formulation by unrolling iterations of an optimization algorithm, leading to an interpretable and parameter-efficient architecture. The proposed inference framework employs a warm-start strategy based on group independent component analysis, which we found to improve optimization performance. Experiments on a realistic synthetic functional MRI (fMRI) dataset demonstrate that the proposed approach significantly improves latent factor recovery compared with representative classical and probabilistic decomposition benchmarks.
L. Montaldo, R. Borsoi, Sebastian Miron et al.· arXiv.org· 0 citations
A novel cross-domain DL framework for MRI reconstruction that leverages graph-based convolutional neural networks to model the autoregressive nature of Fourier features and integrates spatial domain networks and FDNs through a cross-lattice structure, enhancing feature extraction by promoting dense representation through alternating layers.
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A tensor ring alternating least squares with Tikhonov regularization subproblem (TRATR), a framework that incorporates Tikhonov regularization into the core-wise update of the TR-ALS, which demonstrates consistent improvements in relative standard error, peak signal-to-noise ratio (PSNR), and structural similarity index (SSIM).
Recently, tensor-based physics-informed neural networks (T-PINNs) have received increasing attention. However, existing T-PINNs still face a fundamental challenge: they mainly rely on pre-specified low-rank tensor decompositions with manually tuned ranks, which limits their ability to capture the underlying structures of multivariate solution functions and hinders their practical deployment. To address this challenge, we propose a hierarchical rank-evolving (abbreviated as HRE) representation for multivariate functions, which endows us to faithfully capture the underlying structure of the targeted multivariate function accompanying with automatic rank determination. Concretely, in the hierarchical design of HRE representation, the target multivariate function is decomposed as a small-scale inner tensor with a set of univariate functions along each mode, where a customized tensor network decomposition can be readily deployed to capture the underlying structure of the small-scale inner tensor. In HRE representation, the crucial hyperparameters, ranks, can be adaptively revealed during the decomposition, freeing us from manual rank tuning and making HRE practically applicable to real-world problems. Besides, we build the HRE-PINNs correspondingly. Extensive numerical experiments, including high-dimensional static problems (Helmholtz equation and Poisson equation), nonlinear time-dependent problems (Klein-Gordon equation), and complex fluid-dynamics problems (flow mixing equation and Navier-Stokes equation), demonstrate that HRE-PINNs consistently outperform existing state-of-the-art approaches in terms of accuracy.
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This work investigates the use of auxiliary k-space magnitude information for accelerated steady-state dynamic MRI reconstruction, and demonstrates strong consistency of k-space magnitudes across time-frames.
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