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/)
