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Jarvis Haupt Department of Electrical and Computer Engineering University of Minnesota

Compressive Saliency Sensing: Locating Outliers in Large Data Collections from Compressive Measurements. Jarvis Haupt Department of Electrical and Computer Engineering University of Minnesota. Supported by:. TexPoint fonts used in EMF.

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Jarvis Haupt Department of Electrical and Computer Engineering University of Minnesota

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  1. Compressive Saliency Sensing: Locating Outliers in Large Data Collections from Compressive Measurements Jarvis Haupt Department of Electrical and Computer Engineering University of Minnesota Supported by: TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAA

  2. – What’s so Interesting about Sparsity? –

  3. Sparsity and Your Digital Camera Acquire… Original Image Raw Data (Megapixels…) Goldy.jpg (~300kB) Compress… (DWT) Store…

  4. Sparsityin Science and Medicine Wide-field Infrared Survey Explorer (WISE) Functional Magnetic Resonance Imaging (fMRI) Fornax Galaxy Cluster Feb. 17 2010

  5. Sparsity in Communications Are we alone? Sample & DFT Fourier representation… Received signal…

  6. A Sparse Signal Model number of nonzero signal components

  7. Compressed/Compressive Sensing

  8. Sparse Recovery…an Active Area! Convex Optimizations: (Chen, Donoho & Saunders; Donoho; Candes, Romberg, & Tao; Candes & Tao; Wainwright; Zhao & Yu; Yuan & Lin; Chandrasekaran, Recht, Parrilo, & Willsky; Rao, Recht, & Nowak; Wright, Ganesh, Min, & Ma;…) Greedy Methods: (Mallat & Zhang; Pati, Rezaiifar, & Krishnaprasad; Davis, Mallat, & Zhang; Temlyakov; Tropp & Gilbert; Donoho, Tsaig, Drori, & Starck; Needell & Tropp;…) Sketching: (Indyk & Motwani; Indyk; Charikar, Chen, & Farach-Colton; Cormode & Muthukrishnan; Muthukrishnan; Indyk & Gilbert; Berinde; Li, Church, & Hastie;…) Bayesian Approaches: (Tipping; Ji, Xue, & Carin; Ji, Dunson & Carin; Seeger & Nickisch; Wipf, Palmer, & Rao; Vila & Schniter;…) Group Testing: (Dorfman; Feller; Sterrett; Sobel & Groll; Du & Huang; Indyk, Ngo, & Rudra; Gilbert & Strauss; Iwen; Gilbert, Iwen, & Strauss; Emad & Milenkovic; Atia & Saligrama;Cheraghchi, Hormati, Karbasi, & Vetterli; Chan, Che, Jaggi & Saligrama…)

  9. – Beyond Sparsity –

  10. A “Simple” Extension

  11. Recovery of Simple Signals

  12. What’s so “Interesting” about Simple Signals?

  13. – A Generalized Sparse Recovery Task –

  14. Problem Formulation

  15. – Compressive Saliency Sensing – Salient Support Recovery from Compressive Measurements

  16. Assumptions

  17. Some Examples

  18. Approach: Solve a Proxy Problem

  19. Compressive Saliency Sensing

  20. Main Result

  21. – Experimental Results –

  22. – Simple Signals –

  23. Simple Signal – Salient Support Recovery

  24. – An Application in Computer Vision –

  25. Visual Saliency Much MUCH work has been done developing techniques to automatically identify salient regions of a given image: (Itti, Koch, & Niebur, Itti & Koch; Harel, Koch, & Perona; Bruce & Tsotsos, …)

  26. Saliency in Computer Vision

  27. A Generalized form of Sparsity

  28. Subspace Outlier Models for Saliency Vectorize 10x10 patches 100 x 988 matrix Original Image (380x260) (A simplified case of the GMM subspace models used by Yu & Sapiro 2011)

  29. Is This a Good Model for Image Saliency? Prior work exploiting sparse and low-rank models for saliency (Yan, Zhu, Liu & Liu; Shen & Wu;…)

  30. Saliency Maps from Compressive Samples

  31. Saliency Maps from Compressive Samples

  32. Extensions?

  33. – Extra Slides –

  34. Parallel Gigapixel Imagers From H. S. Son, et al., “Design of a spherical focal surface using close packed relay optics,” Optics Express, vol. 19, no. 17, 2011 (Duke University)

  35. MosaicingGigapixel Imagers CAVE Group – Columbia University (www.cs.columbia.edu/CAVE/projects/gigapixel/) dgCam (www.dgcam.org/) GigaPan (www.gigapan.com/)

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