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A Regularization-Guided Equivariant Approach for Image Restoration

CVPR 2025 · Label-efficient and robust learning › Self-supervised and contrastive · approach: Invariance-based self-supervised learning · 3 citations (OpenAlex)

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Proposes EQ-Reg, a self-supervised regularizer that enforces approximate rotation equivariance in intermediate layers of ordinary (non-equivariant) CNNs for image restoration, without changing architecture.

Problem

Strict equivariant CNNs (EQ-CNNs) lose representation accuracy through filter parameterization and impose strict symmetry assumptions that often fail for degraded real-world images, which hurts image restoration.

Approach

Add a layer-wise regularization loss that compares feature maps of rotated-then-convolved inputs with convolved-then-rotated features (spatial rotation plus cyclic channel shift), letting a standard CNN learn an adaptive, approximate rotation equivariance from data while keeping full representational accuracy.

Key results

• On synthesized DeepLesion metal artifact reduction, ACDNet-reg reaches 42.07 average PSNR vs 41.33 for ACDNet, and OSCNet-reg reaches 43.00 vs 42.63 for OSCNet.
• On Rain100H, RCDNet-reg achieves 31.64 PSNR / 0.9138 SSIM, above RCDNet (31.51) and its strict-equivariant variants.
• On CIFAR-100 with SE(2) t=4, EQ-Reg reaches 56.10% accuracy vs 53.28% for Partial-GCNN and 49.79% for GCNN.

Measured effects reported in the paper

Surprising findings

• Replacing standard CNN layers with strictly rotation-equivariant versions generally lowered restoration performance, suggesting the data symmetry is imperfect.
• Strict equivariant variants built on PDO-eConv and E2-CNN degraded notably due to low filter representation accuracy.

Limitations

• Only rotation equivariance (p4 / t=2 or t=4 groups) is studied; other transformations are left to future work.
• Gains over strict equivariant baselines are modest in several settings (e.g., small PSNR gains on metal artifact reduction), and some comparisons are single-run tables without variance reported for most entries.

Experimental setup

Datasets: DeepLesion Rain100L Rain100H Rain1400 Rain12 Urban100 CIFAR-100

Benchmarks: DeepLesion (synthesized metal artifacts) Rain100L Rain100H Rain1400 Rain12 Urban100 inpainting CIFAR-100

Metrics: PSNR SSIM classification accuracy

Baselines: ACDNet DICDNet OSCNet RCDNet GCNN E2-CNN PDO-eConv F-Conv Partial-GCNN IDT Robust EI/REI

Builds on: group equivariant CNN E2-CNN data augmentation Partial-GCNN Fourier-series filter parameterization (F-Conv)

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