An unsupervised method for MRI recovery: Deep image prior with structured sparsity

TL;DR

This work addresses the challenge of reconstructing dynamic MRI from undersampled data by introducing DISCUS, an unsupervised extension of the deep image prior (DIP) that employs a static latent code and frame-specific dynamic codes under a group-sparsity penalty to discover a temporal manifold. The method is validated through four studies, including dynamic phantom simulations and both retrospective and prospective single-shot LGE cardiac MRI data, showing that DISCUS consistently improves NMSE and SSIM compared to CS, L+S, DIP, and SG-DIP, and yields higher expert reader scores. By avoiding reliance on fully sampled training data, DISCUS offers a practical approach for fast, motion-robust cardiac MRI and potentially other single-shot applications, with manifold dimensionality learned directly from data. The results demonstrate that structured sparsity in the latent code space enables effective joint reconstruction of frame sequences, outperforming established baselines and providing a pathway toward clinically viable unsupervised MRI reconstruction.

Abstract

Objective: To propose and validate an unsupervised MRI reconstruction method that does not require fully sampled k-space data. Materials and Methods: The proposed method, deep image prior with structured sparsity (DISCUS), extends the deep image prior (DIP) by introducing group sparsity to frame-specific code vectors, enabling the discovery of a low-dimensional manifold for capturing temporal variations. \discus was validated using four studies: (I) simulation of a dynamic Shepp-Logan phantom to demonstrate its manifold discovery capabilities, (II) comparison with compressed sensing and DIP-based methods using simulated single-shot late gadolinium enhancement (LGE) image series from six distinct digital cardiac phantoms in terms of normalized mean square error (NMSE) and structural similarity index measure (SSIM), (III) evaluation on retrospectively undersampled single-shot LGE data from eight patients, and (IV) evaluation on prospectively undersampled single-shot LGE data from eight patients, assessed via blind scoring from two expert readers. Results: DISCUS outperformed competing methods, demonstrating superior reconstruction quality in terms of NMSE and SSIM (Studies I--III) and expert reader scoring (Study IV). Discussion: An unsupervised image reconstruction method is presented and validated on simulated and measured data. These developments can benefit applications where acquiring fully sampled data is challenging.

Figures (7)

• Figure 1: (a) Overview of the DISCUS framework: A U-Net $\mathcal{\boldsymbol{G}}_{\boldsymbol{\theta}}$ is fed one static $\boldsymbol{z}_0$ and a dynamic $\boldsymbol{z}_{t}$ code vector to generate an estimate of the frame $\boldsymbol{x}_{t}$, which is made consistent with the measured data $\boldsymbol{y}_{t}$. The training is sequentially repeated for all frames in the image series. (b) An example of dynamic code vectors $\boldsymbol{z}_{(1:T)}$ before (left) and after (right) training.The support of the dynamic code vectors, i.e., the number of non-zero entries in the temporal union of $\boldsymbol{z}_{(1:T)}$ (one in this case), defines the dimensionality of the manifold. These non-zero entries generate the temporal variation in the image series.
• Figure 2: Representative results from the Shepp-Logan phantom (Study I). First row shows an example frame with reference image (left) and reconstructions by CS, L+S, DIP, SG-DIP, and DISCUS, from the series containing both rotations and translations. The second row contains the sampling pattern (left) where frequency-encoding is not displayed, and $\times 5$ error maps associated with reconstructions in the first row.
• Figure 3: Representative results from the simulated LGE (Study II) exhibiting a pronounced myocardial scar at $R=4$. First row shows an example frame with reference (left) and reconstructions by CS, L+S, DIP, SG-DIP and DISCUS. Second row contains the GRO sampling pattern (left) where frames are displayed left-to-right, phase encoding is shown top-to-bottom, and frequency encoding is omitted, and $\times 5$ error maps. The final row provides a zoomed-in view of the red box in first row, with the red arrows pointing to the scar.
• Figure 4: Representative results from the ablation study of the simulated LGE (Study II) exhibiting a pronounced myocardial scar at $R=4$. First row shows an example frame with reference (left) and reconstructions by L+S, DGS, and DISCUS with 8, 16, and 32 frames. Second row contains the GRO sampling pattern (left) where frames are displayed left-to-right, phase encoding is shown top-to-bottom, and frequency encoding is omitted, and $\times 5$ error maps. The final row provides a zoomed-in view of the red box in first row, with the red arrows pointing to the scar.
• Figure 5: Representative results from the retrospective patient LGE (Study III) at $R=4$. First row shows an example frame from one of the 8 patients with reference (left) and reconstructions by CS, L+S, DIP, SG-DIP and DISCUS. Second row contains the GRO sampling pattern (left) where frames are displayed left-to-right, phase encoding is shown top-to-bottom, and frequency encoding is not displayed, and $\times 5$ error maps. The final row provides a zoomed-in view of the red box in first row, with the artifact in L+S reconstruction highlighted by red arrow.