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Boosting of Implicit Neural Representation-based Image Denoiser

Zipei Yan, Zhengji Liu, Jizhou Li

TL;DR

This work tackles overfitting in implicit neural representations (INRs) for image denoising by introducing an iterative substitution (ITS) regularization that progressively improves the supervision signal's signal-to-noise ratio (SNR). ITS updates the supervision with $\hat{y}^{i+1} = \frac{y + \hat{x}^i}{2}$ at selected iterations, and a theoretical analysis shows $\text{SNR}(\hat{y}^{i+1}) > \text{SNR}(y)$ under mild conditions. Empirical results on Set9 and Set11 demonstrate that ITS significantly boosts the denoising performance of INR variants (DIP, SIREN, WIRE) across various noise levels, with notable PSNR/SSIM gains and reduced residual noise in error maps. The method is simple, incurs near-zero overhead, and is broadly applicable to INR-based denoising, with future work including extensions to video denoising and more general inverse problems.

Abstract

Implicit Neural Representation (INR) has emerged as an effective method for unsupervised image denoising. However, INR models are typically overparameterized; consequently, these models are prone to overfitting during learning, resulting in suboptimal results, even noisy ones. To tackle this problem, we propose a general recipe for regularizing INR models in image denoising. In detail, we propose to iteratively substitute the supervision signal with the mean value derived from both the prediction and supervision signal during the learning process. We theoretically prove that such a simple iterative substitute can gradually enhance the signal-to-noise ratio of the supervision signal, thereby benefiting INR models during the learning process. Our experimental results demonstrate that INR models can be effectively regularized by the proposed approach, relieving overfitting and boosting image denoising performance.

Boosting of Implicit Neural Representation-based Image Denoiser

TL;DR

This work tackles overfitting in implicit neural representations (INRs) for image denoising by introducing an iterative substitution (ITS) regularization that progressively improves the supervision signal's signal-to-noise ratio (SNR). ITS updates the supervision with at selected iterations, and a theoretical analysis shows under mild conditions. Empirical results on Set9 and Set11 demonstrate that ITS significantly boosts the denoising performance of INR variants (DIP, SIREN, WIRE) across various noise levels, with notable PSNR/SSIM gains and reduced residual noise in error maps. The method is simple, incurs near-zero overhead, and is broadly applicable to INR-based denoising, with future work including extensions to video denoising and more general inverse problems.

Abstract

Implicit Neural Representation (INR) has emerged as an effective method for unsupervised image denoising. However, INR models are typically overparameterized; consequently, these models are prone to overfitting during learning, resulting in suboptimal results, even noisy ones. To tackle this problem, we propose a general recipe for regularizing INR models in image denoising. In detail, we propose to iteratively substitute the supervision signal with the mean value derived from both the prediction and supervision signal during the learning process. We theoretically prove that such a simple iterative substitute can gradually enhance the signal-to-noise ratio of the supervision signal, thereby benefiting INR models during the learning process. Our experimental results demonstrate that INR models can be effectively regularized by the proposed approach, relieving overfitting and boosting image denoising performance.
Paper Structure (9 sections, 2 theorems, 10 equations, 2 figures, 2 tables)

This paper contains 9 sections, 2 theorems, 10 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Preliminary
  3. Proposed Algorithm
  4. Experiments
  5. Experimental Setup
  6. Experimental Results
  7. Ablation Study
  8. Conclusion
  9. REFERENCES

Key Result

Theorem 1

Assuming the model $f_{\theta}(\cdot)$ is converged by minimizing Eq.eq:loss during the SGD optimization within $T$ iterations, then for any iteration $i$ satisfies $1 \ll i \ll T$, the above substitution from Eq.eq:replace can improve the SNR of the supervision signal, i.e., $\text{SNR}(\bm{\hat{y}

Figures (2)

  • Figure 1: Visualization of denoised results on Lena with $\sigma$=25. Each denoised result is quantified by PSNR and SSIM. Besides, each reconstruction error map is calculated from Eq.\ref{['eq:denoised']}, where $\hat{\sigma}$ indicates the noise level estimated by a robust wavelet-based estimator.
  • Figure 2: Impact of hyper-parameter: $N$. Experiments on Lena with $\sigma=25$, and select $N \in \{100, 200, 300, 400\}$.

Theorems & Definitions (4)

  • Theorem 1
  • proof
  • Remark
  • Corollary 1.1