Research map / Architectures and efficiency / RNNs and normalization
i-DEQ: A stable inertial Deep Equilibrium model for image restoration
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes i-DEQ, an inertial, restarted deep equilibrium model that learns an explicit nonconvex regularizer (GS-Denoiser based) and uses momentum in fixed-point iterations to stabilize training and cut inference time 2-5x for image restoration.
Problem
Deep equilibrium models for image restoration are computationally expensive at inference and prone to training instability, with fixed-point solvers needing many iterations.
Approach
Embed inertial extrapolation with adaptive restart inside the DEQ fixed-point iterations of an explicit learned-energy (GS-Denoiser) RED/PnP-style operator, using it both during training and inference, giving convergence guarantees to critical points and faster equilibrium computation.
Key results
- On CS-MRI x8, i-DEQ-P reaches 28.28 dB PSNR / 0.63 SSIM in 78 s versus ELDER's 28.20 dB in 319 s.
- On inpainting sigma=1/255, i-DEQ-P achieves 35.95 dB PSNR vs 34.90 for ELDER and 33.87 for RISP.
- On Rician denoising sigma=0.05, i-DEQ reaches 35.46 dB, +4.13 dB over RISP; ELDER training fails.
Surprising findings
- ELDER training diverges or fails in inpainting at sigma=5/255 and in Rician denoising, while the inertial variant remains trainable.
- Classical DEQ without backtracking loses more than 1 dB PSNR, so the stability cost is hidden in the backtracking step.
Limitations
- Training can still be unstable at very high noise levels or ill-conditioned problems (i-DEQ diverges after 35 epochs at sigma=5/255 inpainting).
- Theory requires smooth data-fidelity terms, excluding l1 data fidelity and other nonsmooth formulations.
- Experiments use small datasets (100 training images) and a lightweight GS-DRUNet backbone.
Experimental setup
Datasets: fastMRI knee-singlecoil BSDS500
Benchmarks: fastMRI knee-singlecoil x8 CS-MRI BSDS500 inpainting BSDS500 motion deblurring BSDS500 Rician denoising
Metrics: PSNR SSIM inference time
Baselines: RAM RED RED-P RISP RISP-P ELDER DiffPIR DPS DDRM MoDL VarNet
Builds on: RED RISP ELDER Jacobian-Free Backpropagation Deep Equilibrium Models
Closest papers by meaning
- Deep Equilibrium Diffusion Restoration with Parallel Sampling (CVPR 2024 · similarity 0.89)
- Positive Concave Deep Equilibrium Models (ICML 2024 · similarity 0.86)
- A Variational Perspective on Solving Inverse Problems with Diffusion Models (ICLR 2024 · similarity 0.86)
- InvFusion: Bridging Supervised and Zero-shot Diffusion for Inverse Problems (NeurIPS 2025 · similarity 0.85)
- A Restoration Network as an Implicit Prior (ICLR 2024 · similarity 0.85)
- Certified Robustness for Deep Equilibrium Models via Serialized Random Smoothing (NeurIPS 2024 · similarity 0.84)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.