{"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/bayesian-convolutional-neural-networks-for","title":"Bayesian Convolutional Neural Networks for Compressed Sensing Restoration","arxiv_id":"1811.04356","date":"2019-02-24","proceeding":null,"authors":[],"abstract":"Deep Neural Networks (DNNs) have aroused great attention in Compressed\nSensing (CS) restoration. However, the working mechanism of DNNs is not\nexplainable, thereby it is unclear that how to design an optimal DNNs for CS\nrestoration. In this paper, we propose a novel statistical framework to explain\nDNNs, which proves that the hidden layers of DNNs are equivalent to Gibbs\ndistributions and interprets DNNs as a Bayesian hierarchical model. The\nframework provides a Bayesian perspective to explain the working mechanism of\nDNNs, namely some hidden layers learn a prior distribution and other layers\nlearn a likelihood distribution. Moreover, the framework provides insights into\nDNNs and reveals two inherent limitations of DNNs for CS restoration. In\ncontrast to most previous works designing an end-to-end DNNs for CS\nrestoration, we propose a novel DNNs to model a prior distribution only, which\ncan circumvent the limitations of DNNs. Given the prior distribution generated\nfrom the DNNs, we design a Bayesian inference algorithm to realize CS\nrestoration in the framework of Bayesian Compressed Sensing. Finally, extensive\nsimulations validate the proposed theory of DNNs and demonstrate that the\nproposed algorithm outperforms the state-of-the-art CS restoration methods.","url_abs":"http://arxiv.org/abs/1811.04356v2","url_pdf":"http://arxiv.org/pdf/1811.04356v2.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":"bayesian-convolutional-neural-networks-for","repo_url":"https://github.com/EthanLan/BCNN","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"bayesian-inference","task_name":"Bayesian Inference"},{"task_slug":"compressed-sensing","task_name":"compressed sensing"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}