PrIINeR: Prior-Informed INR MRI Reconstruction

• The paper introduces PrIINeR, a hybrid method that fuses a population-trained deep prior with instance-specific implicit neural representation to mitigate artifacts in accelerated MRI.
• It employs a continuous coordinate-based model combined with dual k-space consistency constraints, ensuring alignment with both acquired data and prior-informed estimates.
• Empirical results demonstrate significant improvements in SSIM and PSNR on the fastMRI dataset, preserving fine structural details even under high acceleration rates.

Searching arXiv for the specified PrIINeR paper and closely related MRI INR work. PrIINeR is an INR-based MRI reconstruction method for accelerated magnetic resonance imaging that integrates prior knowledge from pre-trained deep learning models into an implicit neural representation framework. It is designed for settings in which acceleration reduces scan time but degrades image quality, especially at high acceleration factors where conventional INRs can suffer from weak prior constraints, structural loss, and aliasing artefacts. In PrIINeR, a population-trained network provides a smooth, artifact-free prior, while instance-wise INR fitting enforces dual consistency with both acquired k-space data and the prior-informed reconstruction (Hemidi et al., 11 Aug 2025).

1. Definition and conceptual position

PrIINeR, short for “Towards Prior-Informed Implicit Neural Representations for Accelerated MRI,” represents the unknown MR image as a continuous function and couples that representation to a learned prior derived from a pre-trained reconstruction network. The method is explicitly framed as a bridge between deep learning and INR-based techniques: it combines population-level knowledge with instance-based optimization and uses dual data consistency to align the reconstruction with both the measured acquisition and the prior estimate (Hemidi et al., 11 Aug 2025).

The central problem addressed by PrIINeR is the failure mode of INR-based MRI reconstruction at high acceleration factors. The stated diagnosis is that standard INRs, while promising for MRI reconstruction, can be under-constrained, which leads to structural loss and aliasing artefacts. PrIINeR addresses this by importing prior information from a deep model before solving the instance-specific inverse problem.

A common misconception is to treat PrIINeR as a purely learning-based reconstructor in the same sense as an end-to-end feed-forward model. The method is instead hybrid: the prior comes from a population-trained network, but reconstruction remains instance-wise and is governed by an explicit optimization objective. This hybridization is one of its defining design choices rather than an implementation detail.

2. INR formulation and image parameterization

The image model in PrIINeR is a continuous implicit neural representation

$I_\theta:\mathbb{R}^2 \to \mathbb{R},$

parameterized by network weights $\theta$. For a normalized spatial coordinate $x=(x_1,x_2)\in[-1,1]^2$, the reconstruction is written as

$I_\theta(x)=f_\theta(\gamma(x)),$

where $\gamma(x)\in\mathbb{R}^D$ is a high-frequency positional encoding and $f_\theta$ is an MLP (Hemidi et al., 11 Aug 2025).

The positional encoding is specified as a multi-level hash-grid, following the Instant NGP style described in the data. The reconstruction network itself is an MLP with three hidden layers of 64 units each, ReLU activations, and a single linear output for the image intensity. In expanded form, the network computes

$$h^{(0)}=\gamma(x),\qquad h^{(\ell+1)}=\mathrm{ReLU}\bigl(W^{(\ell)}h^{(\ell)}+b^{(\ell)}\bigr)\quad(\ell=0,1,2),$$

followed by

$I_\theta(x)=W^{(3)}h^{(3)}+b^{(3)}.$

This parameterization places PrIINeR within the INR family but does not leave the representation unconstrained. A plausible implication is that the continuous coordinate-based model contributes flexibility and fine-grained fitting capacity, while the prior and consistency terms prevent the solution from drifting toward structurally implausible images under aggressive undersampling.

The broader INR literature provides relevant context for why such constraints matter. “Disorder-invariant Implicit Neural Representation” introduces a hash-table augmentation to alleviate spectral bias and improve inverse-problem performance, showing that INR expressivity and frequency behavior are strongly affected by the coordinate representation (Zhu et al., 2023). This suggests why PrIINeR emphasizes both a high-frequency encoding and external prior information, although the two methods target different mechanisms.

3. Prior-informed mechanism and dual k-space consistency

Before fitting the INR to a particular slice, PrIINeR applies a population-trained deep network $D$ to the zero-filled image

$$\mathbf{y}_{zf}=\mathcal{F}^{-1}(M\odot \mathbf{y}),$$

producing a prior reconstruction

$\theta$0

This prior is described as smooth and artifact-free (Hemidi et al., 11 Aug 2025).

The prior is enforced in k-space rather than as a simple image-domain penalty. The corresponding loss is

$\theta$1

where $\theta$2 is the number of coils, $\theta$3 is coil $\theta$4’s sensitivity map parameterized by polynomial coefficients $\theta$5, and $\theta$6 is the multi-coil Fourier transform.

PrIINeR imposes two data-consistency constraints. The first is acquired k-space consistency: $\theta$7 The second is prior-aligned consistency: $\theta$8

The overall objective combines these terms with Total Variation regularization: $\theta$9 In the reported experiments, $x=(x_1,x_2)\in[-1,1]^2$0 and $x=(x_1,x_2)\in[-1,1]^2$1 (Hemidi et al., 11 Aug 2025).

The dual-consistency formulation is central to the method’s identity. It does not merely regularize the INR toward a prior image; it constrains the reconstruction simultaneously against the measured undersampled acquisition and a prior-informed k-space target. This suggests that PrIINeR is intended to preserve the adaptivity of per-instance optimization while preventing the INR from overfitting the undersampled measurements in a way that reintroduces artefacts.

4. Architecture, optimization, and implementation

The reported implementation uses default 16-level Instant NGP hash-grid settings for the positional encoding, a 3-layer $x=(x_1,x_2)\in[-1,1]^2$2-unit ReLU MLP for the INR, and 2D polynomial coil maps of degree at most $x=(x_1,x_2)\in[-1,1]^2$3 with learnable coefficients $x=(x_1,x_2)\in[-1,1]^2$4. Optimization uses Adam with learning rate $x=(x_1,x_2)\in[-1,1]^2$5 and no further schedule. Training is instance-wise, with approximately $x=(x_1,x_2)\in[-1,1]^2$6k iterations per slice until convergence (Hemidi et al., 11 Aug 2025).

The implementation notes identify several reproduction-critical hyperparameters: learning rate $x=(x_1,x_2)\in[-1,1]^2$7, Adam, $x=(x_1,x_2)\in[-1,1]^2$8, $x=(x_1,x_2)\in[-1,1]^2$9, and the $I_\theta(x)=f_\theta(\gamma(x)),$0-unit MLP with default hash-grid encoding. All methods were implemented in PyTorch and run on a single NVIDIA A100 (80 GB) GPU. Code and pretrained models are publicly available at the repository specified in the source paper.

The method also depends on the choice of prior generator. The experiments instantiate plug-in priors from U-Net, GenINR, and ReconFormer, denoted PrIINeR-UNet, PrIINeR-GenINR, and PrIINeR-ReconFormer. This plug-in design indicates that the framework is not tied to a single upstream prior model; rather, it provides a mechanism for coupling different population-trained reconstructors to an INR refinement stage.

A plausible implication is that PrIINeR separates two roles often conflated in MRI reconstruction: distributional prior learning and instance-specific inverse-problem solving. The prior network contributes a population-level bias toward anatomically plausible reconstructions, while the INR absorbs slice-specific detail under explicit k-space constraints.

5. Experimental setup and empirical results

PrIINeR was evaluated on the NYU fastMRI knee dataset with $I_\theta(x)=f_\theta(\gamma(x)),$1 coils and a $I_\theta(x)=f_\theta(\gamma(x)),$2 volume split. The acquisition protocol was retrospective 2D Cartesian undersampling at acceleration factors $I_\theta(x)=f_\theta(\gamma(x)),$3, with $I_\theta(x)=f_\theta(\gamma(x)),$4 central k-space retained. The reported test metrics are SSIM (%) and PSNR (dB) (Hemidi et al., 11 Aug 2025).

The benchmark set includes Zero-filled, IMJENSE Acoeff / Hash as pure INR baselines, U-Net in a segResNet-style configuration, ReconFormer as a transformer-based method, and GenINR as a hybrid INR+CNN approach. Against this set, the paper reports that PrIINeR not only outperforms state-of-the-art INR-based approaches but also improves upon several learning-based state-of-the-art methods (Hemidi et al., 11 Aug 2025).

At $I_\theta(x)=f_\theta(\gamma(x)),$5, PrIINeR-ReconFormer achieves

• SSIM $I_\theta(x)=f_\theta(\gamma(x)),$6
• PSNR $I_\theta(x)=f_\theta(\gamma(x)),$7 dB

and is described as consistently outperforming all INR baselines while raising weaker priors to near state-of-the-art. Across $I_\theta(x)=f_\theta(\gamma(x)),$8, the gains remain significant with $I_\theta(x)=f_\theta(\gamma(x)),$9 in Wilcoxon tests (Hemidi et al., 11 Aug 2025).

The qualitative observations reported in the paper are equally specific. Fine structural details, including ligament boundaries and cartilage, are better preserved than in pure deep nets. Residual aliasing is virtually eliminated compared to standalone INRs. Difference maps in Jet colormap show the lowest errors in PrIINeR, especially around high-contrast edges.

These results support the method’s stated purpose: preserving structure and fidelity while removing aliasing artefacts under aggressive acceleration. They also indicate that prior-informed INR refinement is effective not only when the prior is already strong, but also when the upstream prior is comparatively weak.

6. Related methods, interpretation, and acronym usage

PrIINeR belongs to a broader class of reconstruction methods that combine coordinate-based signal models with additional structure. In INR research more generally, DINER augments a traditional INR backbone with a full-resolution hash table and argues that re-arranging coordinates can alleviate spectral bias, with experiments spanning image fitting, video representation, phase recovery, refractive-index recovery, and NeRF-style synthesis (Zhu et al., 2023). While PrIINeR does not use DINER’s disorder-invariant mapping, both methods reflect the same general pressure in INR research: raw coordinate-based fitting is often insufficient without stronger representational or prior constraints.

Within accelerated MRI specifically, PrIINeR is distinguished by the exact combination of components stated in the source: a pre-trained deep prior, instance-based INR optimization, and dual k-space consistency. It is therefore not simply an INR with an image-domain regularizer, nor merely a deep-network post-processor.

The acronym also has an unrelated use in detector physics. In “Primary track recovery in high-definition gas time projection chambers,” PrIINeR denotes a model-based deconvolution algorithm for recovering a 3D primary track from 2.5D nuclear-recoil readout in gas TPCs (Lewis et al., 2021). That usage is technically unrelated to MRI reconstruction. In the MRI literature, however, PrIINeR refers specifically to the prior-informed INR framework for accelerated reconstruction (Hemidi et al., 11 Aug 2025).

Taken as a whole, the method is best understood as a hybrid reconstruction strategy in which a smooth, artifact-free population prior is fused with per-instance coordinate-based optimization under explicit k-space constraints. The reported outcome is high-fidelity, structurally accurate reconstruction even at high acceleration factors, with statistically significant gains across multiple undersampling regimes and a clear reduction of aliasing artefacts (Hemidi et al., 11 Aug 2025).