Jarvis Haupt Department of Electrical and Computer Engineering University of Minnesota
description
Transcript of Jarvis Haupt Department of Electrical and Computer Engineering University of Minnesota
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/)