Jarvis Haupt Department of Electrical and Computer Engineering University of Minnesota Compressive Saliency Sensing: Locating Outliers in Large Data Collections.

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Presentation transcript:

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

– What’s so Interesting about Sparsity? –

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

Sparsity in Science and Medicine Wide-field Infrared Survey Explorer (WISE) Fornax Galaxy Cluster Feb Functional Magnetic Resonance Imaging (fMRI)

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

A Sparse Signal Model number of nonzero signal components

Compressed/Compressive Sensing

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…) Sparse Recovery…an Active Area!

– Beyond Sparsity –

A “Simple” Extension

Recovery of Simple Signals

What’s so “Interesting” about Simple Signals?

– A Generalized Sparse Recovery Task –

Problem Formulation

– Compressive Saliency Sensing – Salient Support Recovery from Compressive Measurements

Assumptions

Some Examples

Approach: Solve a Proxy Problem

Compressive Saliency Sensing

Main Result

– Experimental Results –

– Simple Signals –

Simple Signal – Salient Support Recovery

– An Application in Computer Vision –

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, …)

Saliency in Computer Vision

A Generalized form of Sparsity

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

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

Saliency Maps from Compressive Samples

Extensions?

– Extra Slides –

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)

Mosaicing Gigapixel Imagers CAVE Group – Columbia University ( GigaPan ( dgCam (