{"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/deep-learning-in-the-wavelet-domain","title":"Deep Learning in the Wavelet Domain","arxiv_id":"1811.06115","date":"2018-11-14","proceeding":null,"authors":["Fergal Cotter","Nick Kingsbury"],"abstract":"This paper examines the possibility of, and the possible advantages to\nlearning the filters of convolutional neural networks (CNNs) for image analysis\nin the wavelet domain. We are stimulated by both Mallat's scattering transform\nand the idea of filtering in the Fourier domain. It is important to explore new\nspaces in which to learn, as these may provide inherent advantages that are not\navailable in the pixel space. However, the scattering transform is limited by\nits inability to learn in between scattering orders, and any Fourier domain\nfiltering is limited by the large number of filter parameters needed to get\nlocalized filters. Instead we consider filtering in the wavelet domain with\nlearnable filters. The wavelet space allows us to have local, smooth filters\nwith far fewer parameters, and learnability can give us flexibility. We present\na novel layer which takes CNN activations into the wavelet space, learns\nparameters and returns to the pixel space. This allows it to be easily dropped\nin to any neural network without affecting the structure. As part of this work,\nwe show how to pass gradients through a multirate system and give preliminary\nresults.","url_abs":"http://arxiv.org/abs/1811.06115v1","url_pdf":"http://arxiv.org/pdf/1811.06115v1.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":"deep-learning-in-the-wavelet-domain","repo_url":"https://github.com/fbcotter/dtcwt_gainlayer","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"deep-learning","task_name":"Deep Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}