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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. 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 Shubhangi. . Saraf. Rutgers University. Based on joint works with . Albert Ai, . Zeev. . Dvir. , . Avi. . Wigderson. Sylvester-. Gallai. Theorem (1893). v. v. v. v. Suppose that every line through . Multi-scale Low Rank Reconstruction for Dynamic Contrast Enhanced Imaging. Frank Ong. 1. , Tao Zhang. 2. , Joseph Cheng. 2. , Martin Uecker. 1. and Michael Lustig. 1. Contact: . frankong@berkeley.edu. Stafford. Mentor: Alex . Cloninger. Directed Reading Project. May 3, 2013. Compressive Sensing & Applications. What is Compressive Sensing?. Signal Processing: . . Acquiring measurements of a . signal. . Sparse matrix data structures, graphs. , manipulation. Xiaoye . Sherry Li. Lawrence Berkeley National . Laboratory. , . USA. xsli@. lbl.gov. crd-legacy.lbl.gov. /~. xiaoye. /G2S3. /. 4. th. Gene . Matrix Algebra and the ANOVA. Matrix properties. Types of matrices. Matrix operations. Matrix algebra in Excel. Regression using matrices. ANOVA in matrix notation. Definition of a . Matrix. a . matrix. Shubhangi. . Saraf. Rutgers University. Based on joint works with . Albert Ai, . Zeev. . Dvir. , . Avi. . Wigderson. Sylvester-. Gallai. Theorem (1893). v. v. v. v. Suppose that every line through . 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. Stafford. Mentor: Alex . Cloninger. Directed Reading Project. May 3, 2013. Compressive Sensing & Applications. What is Compressive Sensing?. Signal Processing: . . Acquiring measurements of a . signal. 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. All Lectures. David Woodruff. IBM Almaden. Massive data sets. Examples. Internet traffic logs. Financial data. etc.. Algorithms. Want nearly linear time or less . Usually at the cost of a randomized approximation. 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. What is a matrix?. A Matrix is just rectangular arrays of items. A typical . matrix . is . a rectangular array of numbers arranged in rows and columns.. Sizing a matrix. By convention matrices are “sized” using the number of rows (m) by number of columns (n).. Efficient Algorithms for Sparse . Recovery . Problems. Sidharth Jaggi. The Chinese University of Hong Kong. Sheng. . Cai. Mayank Bakshi. Minghua Chen. 1. Sparse Recovery. Compressive Sensing. Network Tomography.