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Compressive Saliency Sensing: Locating Outliers in Large Data Collections

This paper explores the use of compressive sensing techniques to locate outliers in large data collections. It discusses various methods such as convex optimizations, greedy methods, sketching, Bayesian approaches, and group testing. The paper also presents an application in computer vision for salient support recovery using compressive saliency sensing.

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Compressive Saliency Sensing: Locating Outliers in Large Data Collections

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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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