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Abstract
In this paper, we present Adaptive Hierarchical Sensing (AHS), a novel adaptive hierarchical sensing algorithm for sparse signals. For a given but unknown signal with a sparse representation in an orthogonal basis, the sensing task is to identify its nonzero transform coefficients by performing only few measurements. A measurement is simply the inner product of the signal and a particular measurement vector. During sensing, AHS partially traverses a binary tree and performs one measurement per visited node. AHS is adaptive in the sense that after each measurement a decision is made whether the entire subtree of the current node is either further traversed or omitted depending on the measurement value. In order to acquire an N dimensional signal that is Ksparse, AHS performs O(K log N/K) measurements. With AHS, the signal is easily reconstructed by a basis transform without the need to solve an optimization problem. When sensing fullsize images, AHS can compete with a stateoftheart compressed sensing approach in terms of reconstruction performance versus number of measurements. Additionally, we simulate the sensing of image patches by AHS and investigate the impact of the choice of the sparse coding basis as well as the impact of the tree composition..
Original language  English 

Title of host publication  Human Vision and Electronic Imaging XIX 
Editors  Bernice E. Rogowitz, Thrasyvoulos N. Pappas, Huib de Ridder 
Number of pages  8 
Volume  9014 
Publisher  SPIE 
Publication date  25.02.2014 
Pages  15:18 
ISBN (Print)  9780819499318 
DOIs  
Publication status  Published  25.02.2014 
Event  Human Vision and Electronic Imaging 2014  San Francisco, California, United States Duration: 03.02.2014 → 06.02.2014 http://hvei.eecs.northwestern.edu/past.html 
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 1 Finished

Learning Efficient Sensing for Active Vision (Esensing)
01.10.11 → 30.09.16
Project: DFG Funding › DFG: Joint Research