Dynamic MRI Reconstruction Via Dual Deep Priors and Low-Rank Plus Sparse Modeling

Dynamic MRI reconstruction from undersampled measurements is a challenging inverse problem that requires preserving both spatial reconstruction quality and temporal consistency across the frames of the cine series. While recent learning-based approaches achieve strong performance, they heavily rely on large training, mostly fully sampled, datasets, and may otherwise generalize poorly. In contrast, training-data-free methods such as deep image prior (DIP) adapt directly to individual scans but often fail to fully exploit temporal structure and are prone to overfitting. They are particularly attractive for dynamic MRI due to the limited large, public, high-quality datasets. In this work, we propose a structured DIP framework for dynamic MRI reconstruction that explicitly models spatiotemporal correlations through a low-rank plus sparse (L+S) decomposition. Instead of directly reconstructing the cine image series, we parameterize the low-rank background and sparse dynamic components using two DIP untrained convolutional neural networks, jointly optimized using accelerated extrapolated ADMM (eADMM). This formulation combines the implicit regularization of DIP with the interpretability of classical L+S regularization. We provide a convergence analysis for the proposed eADMM algorithm in the presence of DIP-based nonconvex parameterizations. In particular, we establish a sufficient descent property and show that every cluster point of the generated sequence is a critical point of the associated Lyapunov function. Across various acceleration factors, our numerical results demonstrate that the proposed method consistently outperforms classical reconstruction and existing supervised and unsupervised MRI reconstruction techniques.

Scan-Adaptive Dynamic MRI Undersampling Using a Dictionary of Efficiently Learned Patterns

Cardiac MRI is limited by long acquisition times, which can lead to patient discomfort and motion artifacts. We aim to accelerate Cartesian dynamic cardiac MRI by learning efficient, scan-adaptive undersampling patterns that preserve diagnostic image quality. We develop a learning-based framework for designing scan- or slice-adaptive Cartesian undersampling masks tailored to dynamic cardiac MRI. Undersampling patterns are optimized using fully sampled training dynamic time-series data. At inference time, a nearest-neighbor search in low-frequency $k$-space selects an optimized mask from a dictionary of learned patterns. Our learned sampling approach improves reconstruction quality across multiple acceleration factors on public and in-house cardiac MRI datasets, including PSNR gains of 2-3 dB, reduced NMSE, improved SSIM, and higher radiologist ratings. The proposed scan-adaptive sampling framework enables faster and higher-quality dynamic cardiac MRI by adapting $k$-space sampling to individual scans.