PPT-An ALPS’ view of Sparse Recovery

Volkan Cevher volkancevherepflch Laboratory for Information and Inference Systems LIONS httplionsepflch Linear Dimensionality Reduction Compressive sensing nonadaptive measurements. Such matrices has several attractive properties they support algorithms with low computational complexity and make it easy to perform in cremental updates to signals We discuss applications to several areas including compressive sensing data stream Adaptivity. in Sparse Recovery. Piotr. . Indyk. MIT. Joint work . with Eric . Price and David Woodruff, 2011.. Sparse recovery. (approximation theory, statistical model selection, information-based complexity, learning Fourier . Aswin C Sankaranarayanan. Rice University. Richard G. . Baraniuk. Andrew E. Waters. Background subtraction in surveillance videos. s. tatic camera with foreground objects. r. ank 1 . background. s. parse. Structured Sparsity Models. Volkan Cevher. volkan@rice.edu. Sensors. 160MP. 200,000fps. 192,000Hz. 2009 - Real time. 1977 - 5hours. Digital Data Acquisition. Foundation: . Shannon/Nyquist sampling theorem. Compressive Sensing of Videos. Venue. CVPR 2012, Providence, RI, USA. June 16, 2012. Organizers. :. Richard G. . Baraniuk. Mohit. Gupta. Aswin C. Sankaranarayanan. Ashok Veeraraghavan. Part 2: Compressive sensing. Grant Thornton, Nominated Adviser Tel: +44 (0) 20 7383 5100 Colin Aaronson / Jen Clarke www.grant-thornton.co.uk Raja . Giryes. ICASSP 2011. Volkan. Cevher. Agenda. The sparse approximation problem. Algorithms and pre-run guarantees. Online performance guarantees. Performance bound. Parameter selection. 2. Sparse approximation. Recovery. . (. Using . Sparse. . Matrices). Piotr. . Indyk. MIT. Heavy Hitters. Also called frequent elements and elephants. Define. HH. p. φ. . (. x. ) = { . i. : |x. i. | ≥ . φ. ||. x||. p. Adaptivity. in Sparse Recovery. Piotr. . Indyk. MIT. Joint work . with Eric . Price and David Woodruff, 2011.. Sparse recovery. (approximation theory, statistical model selection, information-based complexity, learning Fourier . Compressive. Sensing. Volkan . Cevher. volkan@rice.edu. Marco Duarte. Chinmay Hegde. Richard . Baraniuk. Dimensionality Reduction. Compressive sensing. non-adaptive measurements. Sparse Bayesian learning. Sparse Matrices. Morteza. . Mardani. , Gonzalo . Mateos. and . Georgios. . Giannakis. ECE Department, University of Minnesota. Acknowledgments. : . MURI (AFOSR FA9550-10-1-0567) grant. Ann Arbor, USA. . Jeremy Watt and . Aggelos. . Katsaggelos. Northwestern University. Department of EECS. Part 2: Quick and dirty optimization techniques. Big picture – a story of 2’s. 2 excellent greedy algorithms: . Yi Ma. 1,2. . Allen Yang. 3. John . Wright. 1. CVPR Tutorial, June 20, 2009. 1. Microsoft Research Asia. 3. University of California Berkeley. 2. University of Illinois . at Urbana-Champaign. Afsaneh . Asaei. Joint work with: . Mohammad . Golbabaee. ,. Herve. Bourlard, . Volkan. . Cevher. φ. 21. φ. 52. s. 1. s. 2. s. 3. . s. 4. s. 5. x. 1. x. 2. φ. 11. φ. 42. 2. Speech . Separation Problem.