# Denoising and Regularization via Exploiting the Structural Bias of Convolutional Generators

arXiv: https://arxiv.org/abs/1910.14634 · HTML: https://mlsanity.com/paper/1910.14634/

## Key facts

- Cited by 40 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Oct 2019.

## Built on by (most cited first, 30 of 40)

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- [Theoretical Perspectives on Deep Learning Methods in Inverse Problems](https://mlsanity.com/paper/2206.14373/) (2022)
- [On the Spectral Bias of Convolutional Neural Tangent and Gaussian Process Kernels](https://mlsanity.com/paper/2203.09255/) (2022)
- [Untrained Graph Neural Networks for Denoising](https://mlsanity.com/paper/2109.11700/) (2021)
- [Self-Validation: Early Stopping for Single-Instance Deep Generative Priors](https://mlsanity.com/paper/2110.12271/) (2021)
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- [The Devil is in the Upsampling: Architectural Decisions Made Simpler for Denoising with Deep Image Prior](https://mlsanity.com/paper/2304.11409/) (2023)
- [Analysis of Deep Image Prior and Exploiting Self-Guidance for Image Reconstruction](https://mlsanity.com/paper/2402.04097/) (2024)
- [Principal Components Bias in Over-parameterized Linear Models, and its Manifestation in Deep Neural Networks](https://mlsanity.com/paper/2105.05553/) (2021)
- [Blind Image Deblurring with Unknown Kernel Size and Substantial Noise](https://mlsanity.com/paper/2208.09483/) (2022)
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- [Deep Learning for Accelerated and Robust MRI Reconstruction: a Review](https://mlsanity.com/paper/2404.15692/) (2024)
- [A Deep Learning Method for Simultaneous Denoising and Missing Wedge Reconstruction in Cryogenic Electron Tomography](https://mlsanity.com/paper/2311.05539/) (2023)
- [Predicting the Susceptibility of Examples to Catastrophic Forgetting](https://mlsanity.com/paper/2406.09935/) (2024)
- [Bagged Deep Image Prior for Recovering Images in the Presence of Speckle Noise](https://mlsanity.com/paper/2402.15635/) (2024)
- [Multilook Coherent Imaging: Theoretical Guarantees and Algorithms](https://mlsanity.com/paper/2505.23594/) (2025)
- [Self-diffusion for Solving Inverse Problems](https://mlsanity.com/paper/2510.21417/) (2025)
- [Posterior temperature optimized Bayesian models for inverse problems in medical imaging](https://mlsanity.com/paper/2202.00986/) (2022)
- [Towards Architecture-Agnostic Untrained Network Priors for Image Reconstruction with Frequency Regularization](https://mlsanity.com/paper/2312.09988/) (2023)
- [Unsupervised Training of Convex Regularizers using Maximum Likelihood Estimation](https://mlsanity.com/paper/2404.05445/) (2024)
- [HOIN: High-Order Implicit Neural Representations](https://mlsanity.com/paper/2404.14674/) (2024)
- [A Note on the Regularity of Images Generated by Convolutional Neural Networks](https://mlsanity.com/paper/2204.10588/) (2022)

## Abstract (arXiv)

Convolutional Neural Networks (CNNs) have emerged as highly successful tools for image generation, recovery, and restoration. A major contributing factor to this success is that convolutional networks impose strong prior assumptions about natural images. A surprising experiment that highlights this architectural bias towards natural images is that one can remove noise and corruptions from a natural image without using any training data, by simply fitting (via gradient descent) a randomly initialized, over-parameterized convolutional generator to the corrupted image. While this over-parameterized network can fit the corrupted image perfectly, surprisingly after a few iterations of gradient descent it generates an almost uncorrupted image. This intriguing phenomenon enables state-of-the-art CNN-based denoising and regularization of other inverse problems. In this paper, we attribute this effect to a particular architectural choice of convolutional networks, namely convolutions with fixed interpolating filters. We then formally characterize the dynamics of fitting a two-layer convolutional generator to a noisy signal and prove that early-stopped gradient descent denoises/regularizes. Our proof relies on showing that convolutional generators fit the structured part of an image significantly faster than the corrupted portion.