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Proceedings Paper

Simultaneously sparse and low-rank hyperspectral image recovery from coded aperture compressive measurements via convex optimization
Author(s): Tatiana C. Gélvez; Hoover F. Rueda; Henry Arguello
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Paper Abstract

A hyperspectral image (HSI) can be described as a set of images with spatial information across different spectral bands. Compressive spectral imaging techniques (CSI) permit to capture a 3-dimensional hyperspectral scene using 2 dimensional coded and multiplexed projections. Recovering the original scene from a very few projections can be valuable in applications such as remote sensing, video surveillance and biomedical imaging. Typically, HSI exhibit high correlations both, in the spatial and spectral dimensions. Thus, exploiting these correlations allows to accurately recover the original scene from compressed measurements. Traditional approaches exploit the sparsity of the scene when represented in a proper basis. For this purpose, an optimization problem that seeks to minimize a joint ℓ2 − ℓ1 norm is solved to obtain the original scene. However, there exist some HSI with an important feature which does not have been widely exploited; HSI are commonly low rank, thus only a few number of spectral signatures are presented in the image. Therefore, this paper proposes an approach to recover a simultaneous sparse and low rank hyperspectral image by exploiting both features at the same time. The proposed approach solves an optimization problem that seeks to minimize the ℓ2-norm, penalized by the ℓ1-norm, to force the solution to be sparse, and penalized by the nuclear norm to force the solution to be low rank. Theoretical analysis along with a set of simulations over different data sets show that simultaneously exploiting low rank and sparse structures enhances the performance of the recovery algorithm and the quality of the recovered image with an average improvement of around 3 dB in terms of the peak-signal to noise ratio (PSNR).

Paper Details

Date Published: 17 May 2016
PDF: 11 pages
Proc. SPIE 9840, Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XXII, 98401J (17 May 2016); doi: 10.1117/12.2224358
Show Author Affiliations
Tatiana C. Gélvez, Univ. Industrial de Santander (Colombia)
Hoover F. Rueda, Univ. of Delaware (United States)
Henry Arguello, Univ. Industrial de Santander (Colombia)

Published in SPIE Proceedings Vol. 9840:
Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XXII
Miguel Velez-Reyes; David W. Messinger, Editor(s)

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