[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-128682-en":3,"doc-seo-128682-105":31,"detail-sidebar-cat-0-en-105":92},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":28,"seo_description":14,"update_tm":29,"read_time":30},128682,962084928432,"Emma Wilson","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",8,"Research & Report","Statistical and Machine Learning Methods for Low-Photon Imaging - Doctor of Philosophy Thesis","Image recovery from photon-starved measurements presents a demanding inverse problem across microscopy, medical imaging, astronomy, and defence. This thesis develops specialised statistical and machine learning methods for this setting, beginning with a reflected and regularised Langevin stochastic differential equation (RSDE) based MCMC scheme that enforces non-negativity and mitigates exploding gradients. The RSDE is proved well-posed and exponentially ergodic under mild, verifiable conditions. Subsequent contributions integrate deep generative priors, Bayesian empirical frameworks, and tailored denoising diffusion models, and demonstrate robust performance for deblurring, denoising, and inpainting under binomial, geometric, and Poisson noise.","Statistical and Machine Learning Methods for Low-Photon Imaging  \nSavvas Melidonis  \nSubmitted for the degree of  \nDoctor of Philosophy  \nHeriot-Watt University  \nDepartment of Mathematics,  \nSchool of Mathematical and Computer Sciences.  \nJuly, 2024  \nThe copyright in this thesis is owned by the author. Any quotation from the thesis or use of any of the information contained in it must acknowledge this thesis as the source of the quotation or information.  \nAbstract  \nImage recovery from photon-starved measurements is a challenging problem that arisesin applications ranging from microscopy and medical imaging to astronomy and defence. In this thesis, we propose novel statistical and machine learning methods specialised for this important and difficult class of imaging problems.  \nAs our first contribution, we introduce a new and highly efficient Markov chain Monte Carlo (MCMC) methodology based on a reflected and regularised Langevin stochastic differential equation (RSDE) . This methodology can deal with challenges that arise in low-photon imaging such as hard non-negativity constraints and exploding gradients. We show that the introduced RSDE is well-posed and exponentially ergodic under mild and easily verifiable conditions.  \nIn our second contribution, we make use of advances in deep learning and propose a new Bayesian methodology that can leverage deep generative priors. Deep generative models are accurate but tend to scale poorly to large imaging problems. To address this limitation, we propose to embed a conditional deep generative prior with a super-resolution architecture, which scales more robustly to large problems, within an empirical Bayesian framework. This strategy allows scaling to large problems by simultaneously computing the maximum marginal likelihood estimate (MMLE) of a low-resolution version of the image of interest, and generating Monte Carlo samples from the posterior of the high-resolution image of interest conditionally to the MMLE.  \nIn our third contribution, we propose an inference strategy that leverages as image prior a powerful class of generative models known as denoising diffusion models, which we tailor to solve low-photon imaging inverse problems. Our approach is inspired by a variable splitting algorithm known as the Half-Quadratic-Splitting algorithm and it is highly computationally efficient and robust.  \nFinally, we integrate the proposed RSDE-based MCMC methodology into the PnP framework. This is achieved by assuming that the prior model can be implicitly defined by linking its gradient to a deep denoiser prior. The suggested approach improves on the original MCMC methodology in estimation accuracy.  \nAll proposed approaches are demonstrated with a range of experiments related to image deblurring, denoising, and inpainting under observation noise processes that arise in photon-starved scenarios such as the binomial, geometric and Poisson noise.  \nDedicated to my beloved mother, my unceasingly supportive father,  \nmy irreplaceable brother, and all my Teachers...  \nAcknowledgements  \nI would like to start by thanking my examiners, Damian Clancy (Heriot-Watt University) and Pierre Chainais (Centrale Lille Institut), for their time and care in reading this manuscript. Our discussion during the viva process was valuable and thorough and, for me, counted as an unparalleled experience, a beautiful end to a unique journey.  \nI express my gratitude to my three Teachers, Prof. Marcelo Pereyra, Prof. Konstantinos Zygalakis and Prof. Yoann Altmann, who guided me during this journey. I deliberately refrain from using the term “supervisors”, as it feels as an impersonal term that captures only a specific part of the full picture. They not only have educated me to be an independent professional alone-standing researcher able to talk with confidence and apparent expertise for the work to be presented, but they have also guided me to develop my personality and be a better and smarter person. And I sh","cbCaiuQO2J5aH4k0","https://ap.wps.com/l/cbCaiuQO2J5aH4k0","pdf",27036160,2,1,137,"English","en",105,"# Abstract\n## Proposed RSDE-based MCMC methodology\n## Bayesian deep generative priors with super-resolution\n## Denoising diffusion models for inverse problems\n## Plug-and-Play (PnP) integration\n## Experimental validation and noise models\n# Acknowledgements\n## Examiners and teachers\n## Research team and personal dedication","[{\"question\":\"What is the main problem addressed in the thesis?\",\"answer\":\"The thesis focuses on image recovery from photon-starved measurements, a challenging inverse problem arising in microscopy, medical imaging, astronomy, and defence.\"},{\"question\":\"How does the thesis improve MCMC for low-photon imaging?\",\"answer\":\"It introduces an RSDE-based MCMC methodology that handles hard non-negativity constraints and exploding gradients, and it is proven well-posed and exponentially ergodic.\"},{\"question\":\"What deep learning approaches are used in later contributions?\",\"answer\":\"The thesis develops Bayesian methods leveraging conditional deep generative priors with super-resolution and introduces denoising diffusion models tailored to low-photon imaging inverse problems.\"}]","Statistical and Machine Learning Methods for Low-Photon Imaging - Doctor of Philosophy Thesis | PDF",1786002628,345,{"code":4,"msg":32,"data":33},"ok",{"site_id":25,"language":24,"slug":34,"title":13,"keywords":35,"description":14,"schema_data":36,"social_meta":87,"head_meta":89,"extra_data":91,"updated_unix":29},"statistical-and-machine-learning-methods-for-low-photon-imaging-doctor-of-philosophy-thesis","",{"@graph":37,"@context":86},[38,54,69],{"@type":39,"itemListElement":40},"BreadcrumbList",[41,45,48,51],{"item":42,"name":43,"@type":44,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":46,"name":47,"@type":44,"position":20},"https://docshare.wps.com/document/","Document",{"item":49,"name":12,"@type":44,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":44,"position":53},"https://docshare.wps.com/document/statistical-and-machine-learning-methods-for-low-photon-imaging-doctor-of-philosophy-thesis/128682/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":24,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":42,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-23","2026-08-06",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"What is the main problem addressed in the thesis?","Question",{"text":76,"@type":77},"The thesis focuses on image recovery from photon-starved measurements, a challenging inverse problem arising in microscopy, medical imaging, astronomy, and defence.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"How does the thesis improve MCMC for low-photon imaging?",{"text":81,"@type":77},"It introduces an RSDE-based MCMC methodology that handles hard non-negativity constraints and exploding gradients, and it is proven well-posed and exponentially ergodic.",{"name":83,"@type":74,"acceptedAnswer":84},"What deep learning approaches are used in later contributions?",{"text":85,"@type":77},"The thesis develops Bayesian methods leveraging conditional deep generative priors with super-resolution and introduces denoising diffusion models tailored to low-photon imaging inverse problems.","https://schema.org",{"og:url":52,"og:type":88,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":90,"canonical":52},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":93},[94,98,102,106,111,116,121,124,129,132,136],{"id":21,"doc_module":4,"doc_module_name":47,"category_name":95,"show_sort_weight":96,"slug":97},"Story & Novel",90,"story-novel",{"id":20,"doc_module":4,"doc_module_name":47,"category_name":99,"show_sort_weight":100,"slug":101},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":47,"category_name":103,"show_sort_weight":104,"slug":105},"Exam",70,"exam",{"id":107,"doc_module":4,"doc_module_name":47,"category_name":108,"show_sort_weight":109,"slug":110},5,"Comic",60,"comic",{"id":112,"doc_module":4,"doc_module_name":47,"category_name":113,"show_sort_weight":114,"slug":115},6,"Technology",50,"technology",{"id":117,"doc_module":4,"doc_module_name":47,"category_name":118,"show_sort_weight":119,"slug":120},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":47,"category_name":12,"show_sort_weight":122,"slug":123},30,"research-report",{"id":125,"doc_module":4,"doc_module_name":47,"category_name":126,"show_sort_weight":127,"slug":128},9,"Religion & Spirituality",20,"religion-spirituality",{"id":127,"doc_module":4,"doc_module_name":47,"category_name":130,"show_sort_weight":127,"slug":131},"World Cup","world-cup",{"id":133,"doc_module":4,"doc_module_name":47,"category_name":134,"show_sort_weight":133,"slug":135},10,"Lifestyle","lifestyle",{"id":137,"doc_module":4,"doc_module_name":47,"category_name":138,"show_sort_weight":107,"slug":139},19,"General","general"]