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Rotation-Equivariant Self-Supervised Method in Image Denoising

CVPR 2025 · Architectures and efficiency › CNN design · approach: Steerable rotation-equivariant CNNs · 5 citations (OpenAlex)

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Introduces rotation-equivariant convolutions (Fconv) into self-supervised image denoising (N2N, N2V, R2R) with a theoretical equivariance-error analysis of U-Net, plus an adaptive fusion network (AdaReNet) that blends equivariant and vanilla CNN branches.

Problem

Self-supervised image denoising methods are almost all CNN-based and exploit only translation equivariance; it is unclear whether rotation equivariance can be added to U-Net-based self-supervised denoisers, given up/downsampling and reduced representation accuracy of equivariant networks.

Approach

Replace convolutions in self-supervised denoisers (N2N/N2V U-Nets, R2R DnCNN) with Fourier-series-based rotation-equivariant convolutions, prove bounded rotation-equivariance error for up/downsampling and full U-Net, and adaptively fuse an equivariant branch with a vanilla CNN branch via a learned mask.

Key results

• On N2V with Gaussian25, N2V-EQ+ averages 29.05/0.832 PSNR/SSIM versus 28.08/0.811 for the baseline N2V (Table 2 average).
• N2V equivariant error drops from 0.233 (N2V) to 0.068 (N2V-EQ) and 0.076 (N2V-EQ+), supporting that gains come from reduced equivariance error.
• For N2N at Gaussian50 on Kodak, N2N-EQ+ reaches 28.69 dB vs 28.29 dB for N2N (Table 1).

Measured effects reported in the paper

Surprising findings

• Adaptive EQ+ variant underperforms the pure EQ variant on R2R with small training data, attributed to more adaptive-network parameters.

Limitations

• Equivariant convolutions reduce representation accuracy because of parameter sharing and filter parameterization.
• Natural images do not strictly obey rotation equivariance, motivating the adaptive fusion but also adding parameters.
• Equivariance error of up/downsampling decays only as O(h), slower than convolution's O(h^2).

Experimental setup

Datasets: BSD500 BSD300 Kodak Set14 BSD68

Benchmarks: Kodak BSD300 BSD500 Set14 BSD68

Metrics: PSNR SSIM equivariance error

Baselines: N2N N2V R2R CNN G-CNN E2-CNN PDO-eConv Fconv

Builds on: Noise2Noise Noise2Void Recorrupted-to-Recorrupted Fconv (Xie et al. rotation-equivariant CNN) G-CNN

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