{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/denoising-and-regularization-via-exploiting","title":"Denoising and Regularization via Exploiting the Structural Bias of Convolutional Generators","arxiv_id":"1910.14634","date":"2019-10-31","proceeding":"ICLR 2020 1","authors":["Reinhard Heckel","Mahdi Soltanolkotabi"],"abstract":"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.","url_abs":"https://arxiv.org/abs/1910.14634v2","url_pdf":"https://arxiv.org/pdf/1910.14634v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"denoising-and-regularization-via-exploiting","repo_url":"https://github.com/MLI-lab/overparameterized_convolutional_generators","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"attribute","task_name":"Attribute"},{"task_slug":"denoising","task_name":"Denoising"},{"task_slug":"image-generation","task_name":"Image Generation"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1910.14634","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}