[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-128853-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-128853-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","compressed-sensing-and-bayesian-experimental-design","Compressed Sensing and Bayesian Experimental Design","","Relates compressed sensing with Bayesian experimental design and proposes an efficient approximate method for sequential design optimization using expectation propagation. A large comparative study of linearly measuring natural images shows that measuring wavelet coefficients top-down consistently outperforms random-measurement CS methods, while prior sequential projection optimization performs worse. The approach learns measurement filters directly on full images, outperforming the wavelet heuristic, enables “learning compressed sensing,” generalizes beyond sparsity, and can scale to large signal representations.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/research-report/","Research & Report",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/compressed-sensing-and-bayesian-experimental-design/128853/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/compressed-sensing-and-bayesian-experimental-design/128853.png","ImageObject",300,407,{"name":42,"@type":43},"Aria","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-09-19","2026-08-06",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",9,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"How does the document connect compressed sensing with Bayesian experimental design?","Question",{"text":63,"@type":64},"It frames compressed sensing as a special case within a broader Bayesian experimental design perspective, where signal and algorithm assumptions can be modeled and optimized under uncertainty.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"What experimental finding compares wavelet-based measurements to random CS measurements?",{"text":68,"@type":64},"In comparative experiments on natural images, top-down wavelet coefficient measurements systematically yield better reconstruction than random measurement designs used in CS.",{"name":70,"@type":61,"acceptedAnswer":71},"What is the main contribution of the proposed method?",{"text":72,"@type":64},"The work introduces an efficient approximate sequential Bayesian design method based on expectation propagation, enabling the learning of measurement filters that outperform a standard wavelet heuristic on full images.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},128853,1786003913,{"code":4,"msg":82,"data":83},"success",[84,88,92,96,101,106,111,115,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":93,"show_sort_weight":94,"slug":95},"Exam",70,"exam",{"id":97,"doc_module":4,"doc_module_name":25,"category_name":98,"show_sort_weight":99,"slug":100},5,"Comic",60,"comic",{"id":102,"doc_module":4,"doc_module_name":25,"category_name":103,"show_sort_weight":104,"slug":105},6,"Technology",50,"technology",{"id":107,"doc_module":4,"doc_module_name":25,"category_name":108,"show_sort_weight":109,"slug":110},7,"Healthcare",40,"healthcare",{"id":112,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":113,"slug":114},8,30,"research-report",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":97,"slug":129},19,"General","general",{"code":4,"msg":82,"data":131},{"doc_id":79,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":112,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":112,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":80,"read_time":117},2336474459895,"https://ap-avatar.wpscdn.com/avatar/22000baeef7a5ed0655?x-image-process=image/resize,m_fixed,w_180,h_180&k=1786071322749376916","View metadata, citation and similar [papers at ](papers at core.ac.uk)[core.ac.uk](papers at core.ac.uk) brought to you by CORE  \nprovided by Infoscience- École polytechnique fédérale de Lausanne  \nCompressed Sensing and Bayesian Experimental Design  \nMatthias W. Seeger [seeger@tuebingen.mpg.de](seeger@tuebingen.mpg.de)  \nHannes Nickisch [hn@tuebingen.mpg.de](hn@tuebingen.mpg.de)  \nMax Planck Institute for Biological Cybernetics, Spemannstr. 38, T¨ubingen, Germany  \nAbstract  \nWe relate compressed sensing (CS) with Bayesian experimental design and provide a novel e􀀎cient approximate method for the latter, based on expectation propagation. In a large comparative study about linearly measuring natural images, we show that the simple standard heuristic of measuring wavelet coe􀀎cients top-down systematically outperforms CS methods using random measurements; the sequential projection optimisation approach of (Ji & Carin, 2007) performs even worse. We also show that our own approximate Bayesian method is able to learn measurement 􀀌lters on full images e􀀎ciently which outperform the wavelet heuristic. To our knowledge, ours is the 􀀌rst successful attempt at “learning compressed sensing” for images of realistic size. In contrast to common CS methods, our framework is not restricted to sparse signals, but can readily be applied to other notions of signal complexity or noise models. We give concrete ideas how our method can be scaled up to large signal representations.  \n1. Introduction  \nThere has been a lot of recent interest in the area of compressed sensing (CS) (Cand􀀒es et al., 2006; Donoho, 2006), where it is argued that if signals can be expected to be compressible due to sparseness after some linear transform, then they can be reconstructed from a number of measurements signi􀀌cantly below the Nyquist/Shannon limit, if the measurement design isnot too regular. In this paper, we relate CS to the more general notion of statistical (Bayesian) experimental design.  \nAppearing in Proceedings of the 25 th International Conference on Machine Learning, Helsinki, Finland, 2008 . Copyright 2008 by the author(s)/owner(s) .  \nThrough this view, characteristics of signals and algorithms, de􀀌ned in an abstract mathematical way in the CS literature so far, become understandable and workable. The experimental design approach applies to signals of low complexity in general, not only to sparse ones. It has the potential to clearly outperform the randomised designs, favoured by theoretical CS arguments, in cases where signals are not welldescribed by common CS assumptions. For example, CS has been viewed with some scepticism so far by researchers in computer vision and image statistics (Weiss et al., 2007) . While images exhibit transform sparsity to some degree, purely random measurement designs can be suboptimal for them. The reason is that there is more to low-level image statistics than sparsity. Much of this knowledge can be modeled tractably (Simoncelli, 1999) and could therefore be incorporated into a Bayesian experimental design architecture. To our knowledge, the current CS reconstruction schemes are purely estimation-based and lack proper representations of uncertainty (which is what fundamentally drives experimental design), and the theory deals exclusively with signals which are unstructured except for random sparsity. We present experimental results sheding more light on the relationship between CSand images. Similar to (Weiss et al., 2007), we 􀀌nd that standard approaches to linear image measurement (wavelet coe􀀎cients) give signi􀀌cantly better reconstruction results than using random measurements favoured by CS, even if modern CS reconstruction algorithms are applied. Yet, our experimental evidence is more substantial than theirs. Beyond that, we show that our e􀀎cient approximation to sequential Bayesian design can be used to learn measurements which indeed outperform measuring wavelet coe􀀎cients topdown. Our method provides a practi","cbCaisBVufevvryT","https://ap.wps.com/l/cbCaisBVufevvryT","pdf",371888,"English","# Introduction\n## Compressed sensing and statistical experimental design\n## Sequential Bayesian design and expectation propagation","[{\"question\":\"How does the document connect compressed sensing with Bayesian experimental design?\",\"answer\":\"It frames compressed sensing as a special case within a broader Bayesian experimental design perspective, where signal and algorithm assumptions can be modeled and optimized under uncertainty.\"},{\"question\":\"What experimental finding compares wavelet-based measurements to random CS measurements?\",\"answer\":\"In comparative experiments on natural images, top-down wavelet coefficient measurements systematically yield better reconstruction than random measurement designs used in CS.\"},{\"question\":\"What is the main contribution of the proposed method?\",\"answer\":\"The work introduces an efficient approximate sequential Bayesian design method based on expectation propagation, enabling the learning of measurement filters that outperform a standard wavelet heuristic on full images.\"}]","Compressed Sensing and Bayesian Experimental Design | PDF"]