Simultaneously sparse and low-rank hyperspectral image recovery from coded aperture compressive measurements via convex optimization

Tatiana C. Gélvez; Hoover F. Rueda; Henry Arguello

doi:10.1117/12.2224358

17 May 2016 Simultaneously sparse and low-rank hyperspectral image recovery from coded aperture compressive measurements via convex optimization

Tatiana C. Gélvez, Hoover F. Rueda, Henry Arguello

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Proceedings Volume 9840, Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XXII; 98401J (2016) https://doi.org/10.1117/12.2224358
Event: SPIE Defense + Security, 2016, Baltimore, MD, United States

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 − ℓ₁norm 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).

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Tatiana C. Gélvez, Hoover F. Rueda, and Henry Arguello "Simultaneously sparse and low-rank hyperspectral image recovery from coded aperture compressive measurements via convex optimization", Proc. SPIE 9840, Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XXII, 98401J (17 May 2016); https://doi.org/10.1117/12.2224358

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KEYWORDS

Hyperspectral imaging

Image restoration

Coded apertures

Convex optimization

Computer simulations

Data modeling

Image enhancement

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