Jarvis Haupt

Department of Electrical and Computer Engineering

University of Minnesota

Compressive Saliency Sensing:Locating Outliers in Large Data Collections

from Compressive Measurements

Supported by:

– What’s so Interesting about Sparsity? –

Sparsity and Your Digital Camera

Compress

…

(DW

T)

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. 17 2010

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 automaticallyidentify 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

Saliency Maps from Compressive Samples

Extensions?

– Extra Slides –

Parallel Gigapixel Imagers

FromH. 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 ImagersCAVE Group – Columbia University(www.cs.columbia.edu/CAVE/projects/gigapixel/)

GigaPan(www.gigapan.com/)

dgCam(www.dgcam.org/)