UnrollINR: Zero-Shot MRI Reconstruction

• UnrollINR is a zero-shot, self-supervised fast MRI reconstruction method that operates on scan-specific undersampled k-space without relying on external training data.
• It utilizes a physics-guided unrolled iterative architecture, combining a data consistency step (using conjugate gradient) with an implicit neural representation for regularization.
• The approach demonstrates notable improvements in PSNR and SSIM at high acceleration rates, addressing common issues of domain shift and the scarcity of fully sampled ground truth.

Searching arXiv for the specified paper and closely related MRI reconstruction references. UnrollINR is a zero-shot self-supervised fast MRI reconstruction framework that performs scan-specific reconstruction from undersampled multi-coil k-space without external training data or paired fully sampled targets. It is formulated as a physics-guided unrolled iterative reconstruction model in which data consistency is enforced by the MRI forward model and regularization is supplied by an Implicit Neural Representation (INR). In the reported experiments, the method is designed for 2D fast MRI, uses only the current scan’s undersampled measurements, and is presented as a response to two practical constraints of supervised MRI reconstruction: the difficulty of obtaining fully sampled ground truth at scale and the degradation of out-of-distribution generalization across scanners, anatomies, coil configurations, and sampling patterns (Xu et al., 8 Oct 2025).

1. Problem formulation and zero-shot setting

MRI reconstruction is posed as a regularized inverse problem over undersampled multi-coil k-space. For coil $i$, the acquisition model is

$y_i = M F C_i x + n_i,$

and in stacked form,

$y = Ex + n,$

where $x$ is the target complex-valued image, $y$ is the observed undersampled k-space, $M$ is the undersampling mask, $F$ is the Fourier transform, $C_i$ is coil sensitivity for coil $i$, and $E$ is the full forward encoding operator (Xu et al., 8 Oct 2025).

The corresponding regularized formulation is

$y_i = M F C_i x + n_i,$0

with the first term enforcing data consistency and $y_i = M F C_i x + n_i,$1 encoding prior knowledge. Within this setting, UnrollINR is explicitly introduced as a scan-specific zero-shot self-supervised method. It operates only on the undersampled measurements from the current scan, without any external training set and without fully sampled supervision.

This design addresses the two limitations emphasized in the source paper. First, fully sampled ground truth is expensive or impossible to collect at scale. Second, models trained in a supervised fashion can suffer from degraded performance under domain shift. A plausible implication is that UnrollINR is intended not merely as a training paradigm change, but as a deployment strategy for acquisition settings where matched training distributions are unavailable or unstable.

2. Unrolled architecture and variable splitting

The method adopts a physics-guided unrolled iterative reconstruction architecture based on variable splitting. The optimization problem is reformulated as

$y_i = M F C_i x + n_i,$2

This separates the reconstruction into a regularization step on $y_i = M F C_i x + n_i,$3 and a data consistency step on $y_i = M F C_i x + n_i,$4. The two subproblems are alternated in each unrolled iteration:

$y_i = M F C_i x + n_i,$5

$y_i = M F C_i x + n_i,$6

Each unrolled basic unit therefore has two modules: an INR-based regularization module, which produces $y_i = M F C_i x + n_i,$7, and a data consistency module, which computes the physics-constrained update for $y_i = M F C_i x + n_i,$8 using conjugate gradient (CG) (Xu et al., 8 Oct 2025).

The network input is the zero-filled image

$y_i = M F C_i x + n_i,$9

and the output is the final reconstruction $y = Ex + n,$0. In the reported implementation, increasing the number of unrolled basic units did not significantly improve performance but increased computation, so the method uses 1 basic unit. This is notable because the “unrolled” characterization here refers to the explicit decomposition into prior and data-consistency operators, not to a deep stack of many repeated units.

3. INR regularization and implicit constraints on the solution space

The distinguishing feature of UnrollINR is that the regularizer is an Implicit Neural Representation rather than a CNN denoiser. The INR models the image as a continuous function from spatial coordinates to complex intensity:

$y = Ex + n,$1

To better represent high frequencies, the coordinates are encoded first:

$y = Ex + n,$2

where $y = Ex + n,$3 is a learnable coordinate encoding. In the reconstruction loop, the regularization output is

$y = Ex + n,$4

The paper characterizes this INR as constraining the reconstruction space by restricting $y = Ex + n,$5 to the manifold of images representable by a coordinate-based MLP with learnable encoding (Xu et al., 8 Oct 2025). The stated effects of this implicit bias are smoothness and continuity in image space, preference for structured natural image-like signals, suppression of arbitrary noise and aliasing artifacts, and strong inductive bias even without external data. The paper further argues that the INR’s learning consistency bias functions as implicit regularization, stabilizing the ill-posed reconstruction problem at high acceleration.

To improve fine-detail recovery, UnrollINR uses multi-resolution hash encoding in the style of Instant-NGP. An ablation replacing Instant-NGP hash encoding with DINER reduces performance at $y = Ex + n,$6 from the baseline level to 36.35 PSNR and 0.9314 SSIM, which is presented as evidence that multi-resolution hash encoding helps capture local and high-frequency structure more effectively.

4. Optimization procedure and loss construction

The alternating updates consist of a prior step and a data-consistency step. The prior update is written as

$y = Ex + n,$7

and is approximated in practice by the INR parameterization $y = Ex + n,$8. The data-consistency update is

$y = Ex + n,$9

which yields the normal equation

$x$0

Because $x$1 is not analytically invertible for practical multi-coil MRI, the method solves this step iteratively with CG. The data-consistency module uses 20 CG iterations. Since CG has no trainable parameters, it is described as memory-efficient and compatible with unrolling with little extra memory overhead (Xu et al., 8 Oct 2025).

Training is scan-specific rather than dataset-level. The model is optimized per scan using only the current scan’s undersampled k-space. The optimized parameters include the INR parameters $x$2 and the learnable hyperparameters $x$3 and $x$4. The loss is

$x$5

with

$x$6

and

$x$7

where $x$8 is the gradient operator. The paper notes that the printed expression for $x$9 has a formatting issue, but identifies the intended form as a normalized $y$0-$y$1 discrepancy between measured k-space and predicted k-space. Initial values for the learnable hyperparameters are reported as $y$2, $y$3 in retrospective experiments and $y$4, $y$5 in prospective experiments. Ray Tune + Optuna were used to choose initial values using PSNR as the metric.

5. Experimental configuration, baselines, and quantitative performance

Three datasets are reported. The retrospective experiments use fastMRI knee data with 15 coils and images cropped to $y$6, and fastMRI brain data with 20 coils and images cropped to $y$7. The prospective experiment uses undersampled brain data acquired on a 3T Siemens TIM TRIO scanner with a 12-channel head coil and image size $y$8 (Xu et al., 8 Oct 2025).

Retrospective experiments use random undersampling at $y$9, $M$0, and $M$1. The prospective experiment uses $M$2. Baselines are MoDL, ZS-SSL, IMJENSE, ConvDecoder, and L1-ESPIRiT. Quantitative evaluation uses PSNR and SSIM, accompanied by visual comparisons and error maps.

The strongest quantitative evidence summarized in the source concerns the fastMRI knee retrospective experiment at $M$3.

Method	PSNR	SSIM
UnrollINR	37.72 ± 1.66	0.9429 ± 0.0119
MoDL	33.47 ± 1.19	0.8771 ± 0.0213
ZS-SSL	31.71 ± 1.45	0.8358 ± 0.0357
IMJENSE	32.54 ± 1.53	0.8460 ± 0.0309
ConvDecoder	31.08 ± 1.29	0.8205 ± 0.0280
L1-ESPIRiT	31.47 ± 1.03	0.8361 ± 0.0225

Relative to the strongest baseline in that comparison, MoDL, the reported improvements at $M$4 are about 4.25 dB in PSNR and 0.0658 in SSIM. The paper highlights this comparison because MoDL is supervised, whereas UnrollINR is scan-specific zero-shot. On the knee dataset, UnrollINR is also reported as best at all tested accelerations, with 39.39 PSNR / 0.9606 SSIM at $M$5, 38.68 PSNR / 0.9545 SSIM at $M$6, and 37.72 PSNR / 0.9429 SSIM at $M$7. In the prospective $M$8 experiment, UnrollINR is likewise reported to outperform all baselines, with better artifact suppression and detail preservation.

6. Ablation studies, robustness, and identified limitations

The ablation analyses isolate the contribution of the regularization module, the data-consistency module, the coordinate encoder, the TV term, and the iterative solver configuration (Xu et al., 8 Oct 2025). At $M$9, the reported baseline is 37.58 PSNR and 0.9436 SSIM. Removing regularization yields 31.1 PSNR and 0.8420 SSIM, while removing data consistency yields 33.34 PSNR and 0.8726 SSIM. The reported interpretation is that both components are essential, with the regularization module particularly important.

Removing TV loss reduces performance at $F$0 to 37.00 PSNR and 0.9394 SSIM, indicating an additional but modest contribution to local spatial consistency and edge preservation. Increasing CG iterations improves performance with diminishing returns, and 20 CG iterations are chosen as a trade-off. The method was also tested with uniform, radial, and spiral undersampling at approximately $F$1, where it remained robust and consistently strong; this is presented as evidence of sampling-pattern insensitivity.

Several limitations are stated explicitly. Training and optimization remain relatively slow compared with some other INR-based methods such as IMJENSE. The current INR regularizer relies mainly on coordinate-to-intensity mapping, and richer image-domain encoders could improve efficiency and performance. The approach requires estimation of coil sensitivity maps; ESPIRiT from central k-space is used. The reported implementation is designed for 2D fast MRI, and reconstruction requires per-scan inference or training time because optimization is scan-specific. Potential extensions proposed in the paper include meta-learning for better weight initialization, transfer learning for faster adaptation to new tasks, and alternative INR-based iterative frameworks.

Taken together, these results position UnrollINR as a reconstruction method that combines physical correctness through the forward model, a continuous implicit prior through the INR regularizer, and scan-specific self-supervised optimization. This suggests that its reported advantage at severe undersampling is linked to the interaction between a strongly constrained solution manifold and explicit measurement fidelity, rather than to external data-driven pretraining alone.