{"257471":{"#nid":"257471","#data":{"type":"event","title":"Using structure to solve underdetermined systems of linear equations and overdetermined systems of quadratic equations","body":[{"value":"\u003Cp\u003E\u003Cstrong\u003ESpeaker:\u003C\/strong\u003E\u003C\/p\u003E\u003Cp\u003EDr. Justin Romberg\u003C\/p\u003E\u003Cp\u003E\u003Cem\u003EAssociate Professor, School of Electrical and Computer Engineering,Georgia Institute of Technology\u003C\/em\u003E\u003C\/p\u003E\u003Cp\u003E\u003Cstrong\u003ETitle:\u003C\/strong\u003E\u003C\/p\u003E\u003Cp\u003EUsing structure to solve underdetermined systems of linea\u003C\/p\u003E\u003Cp\u003E\u003Cstrong\u003EAbstract:\u003C\/strong\u003E\u003C\/p\u003E\u003Cp\u003EWe will start by giving a high-level overview of the fundamental results in the field that has come to be known as compressive sensing.\u0026nbsp; The central theme of this body of work is that underdetermined systems of linear equations can be meaningfully \u0022inverted\u0022 if they have structured solutions.\u0026nbsp; Two examples of structure would be if the unknown entity is a vector which is sparse (has only a few \u0022active\u0022 entries) or if it is a matrix which is low rank.\u0026nbsp; We discuss some of the applications of this theory in signal processing and machine learning.\u0026nbsp;\u003C\/p\u003E\u003Cp\u003EIn the second part of the talk, we will show how some of these structured recovery results give us new insights into solving systems of quadratic and bilinear equations.\u0026nbsp; In particular, we will show how recasting classical problems like channel separation and blind deconvolution as a structured matrix factorization gives us new insight into how to solve them.\u003C\/p\u003E\u003Cp\u003E\u003Cstrong\u003EBio:\u003C\/strong\u003E\u003C\/p\u003E\u003Cp\u003EDr. Justin Romberg is an Associate Professor in the School of Electrical and Computer Engineering at the Georgia Institute of Technology.\u0026nbsp; Dr. Romberg received the B.S.E.E. (1997), M.S. (1999) and Ph.D. (2004) degrees from Rice University in Houston, Texas.\u0026nbsp; From Fall 2003 until Fall 2006, he was a Postdoctoral Scholar in Applied and Computational Mathematics at the California Institute of Technology. \u0026nbsp;In the Fall of 2006, he joined the Georgia Tech ECE faculty.\u0026nbsp; In 2009 he received a PECASE award and a Packard Fellowship, and in 2010 he was named a Rice University Outstanding Young Engineering Alumnus.\u0026nbsp; He is currently on the editorial board for the SIAM Journal on Imaging Science.\u003C\/p\u003E","summary":null,"format":"limited_html"}],"field_subtitle":"","field_summary":[{"value":"\u003Cp\u003E\u003Cstrong\u003EAbstract:\u003C\/strong\u003E\u003C\/p\u003E\u003Cp\u003EWe will start by giving a high-level overview of the fundamental results in the field that has come to be known as compressive sensing.\u0026nbsp; The central theme of this body of work is that underdetermined systems of linear equations can be meaningfully \u0022inverted\u0022 if they have structured solutions.\u0026nbsp; Two examples of structure would be if the unknown entity is a vector which is sparse (has only a few \u0022active\u0022 entries) or if it is a matrix which is low rank.\u0026nbsp; We discuss some of the applications of this theory in signal processing and machine learning.\u0026nbsp;\u003C\/p\u003E\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\u003Cp\u003EIn the second part of the talk, we will show how some of these structured recovery results give us new insights into solving systems of quadratic and bilinear equations.\u0026nbsp; In particular, we will show how recasting classical problems like channel separation and blind deconvolution as a structured matrix factorization gives us new insight into how to solve them.\u003C\/p\u003E","format":"limited_html"}],"field_summary_sentence":[{"value":"Big Data Chalk \u0026 Talk \/ Brown Bag"}],"uid":"27838","created_gmt":"2013-11-26 14:39:34","changed_gmt":"2017-04-13 21:23:47","author":"Holly Rush","boilerplate_text":"","field_publication":"","field_article_url":"","field_event_time":{"event_time_start":"2013-12-05T11:00:00-05:00","event_time_end":"2013-12-05T12:30:00-05:00","event_time_end_last":"2013-12-05T12:30:00-05:00","gmt_time_start":"2013-12-05 16:00:00","gmt_time_end":"2013-12-05 17:30:00","gmt_time_end_last":"2013-12-05 17:30:00","rrule":null,"timezone":"America\/New_York"},"extras":[],"groups":[{"id":"1304","name":"High Performance Computing (HPC)"}],"categories":[],"keywords":[{"id":"15092","name":"big data"}],"core_research_areas":[],"news_room_topics":[],"event_categories":[{"id":"1795","name":"Seminar\/Lecture\/Colloquium"}],"invited_audience":[{"id":"78751","name":"Undergraduate students"},{"id":"78761","name":"Faculty\/Staff"},{"id":"174045","name":"Graduate students"}],"affiliations":[],"classification":[],"areas_of_expertise":[],"news_and_recent_appearances":[],"phone":[],"contact":[{"value":"\u003Cp\u003EHolly Rush (404) 385-1043\u003C\/p\u003E","format":"limited_html"}],"email":[],"slides":[],"orientation":[],"userdata":""}}}