HYCA: A New Technique for Hyperspectral Compressive Sensing
Hyperspectral imaging relies on sophisticated acquisition and data processing systems able to acquire, process, store, and transmit hundreds or thousands of image bands from a given area of interest. In this paper, we exploit the high correlation existing among the components of the hyperspectral da...
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| Autor*in: |
Martin, Gabriel [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2015 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: IEEE transactions on geoscience and remote sensing - New York, NY : IEEE, 1964, 53(2015), 5, Seite 2819-2831 |
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| Übergeordnetes Werk: |
volume:53 ; year:2015 ; number:5 ; pages:2819-2831 |
| Links: |
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| DOI / URN: |
10.1109/TGRS.2014.2365534 |
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| 520 | |a Hyperspectral imaging relies on sophisticated acquisition and data processing systems able to acquire, process, store, and transmit hundreds or thousands of image bands from a given area of interest. In this paper, we exploit the high correlation existing among the components of the hyperspectral data sets to introduce a new compressive sensing methodology, termed hyperspectral coded aperture (HYCA), which largely reduces the number of measurements necessary to correctly reconstruct the original data. HYCA relies on two central properties of most hyperspectral images, usually termed data cubes: 1) the spectral vectors live on a low-dimensional subspace; and 2) the spectral bands present high correlation in both the spatial and the spectral domain. The former property allows to represent the data vectors using a small number of coordinates. In this paper, we particularly exploit the high spatial correlation mentioned in the latter property, which implies that each coordinate is piecewise smooth and thus compressible using local differences. The measurement matrix computes a small number of random projections for every spectral vector, which is connected with coded aperture schemes. The reconstruction of the data cube is obtained by solving a convex optimization problem containing a data term linked to the measurement matrix and a total variation regularizer. The solution of this optimization problem is obtained by an instance of the alternating direction method of multipliers that decomposes very hard problems into a cyclic sequence of simpler problems. In order to address the need to set up the parameters involved in the HYCA algorithm, we also develop a constrained version of HYCA (C-HYCA), in which all the parameters can be automatically estimated, which is an important aspect for practical application of the algorithm. A series of experiments with simulated and real data shows the effectiveness of HYCA and C-HYCA, indicating their potential in real-world applications. | ||
| 650 | 4 | |a cyclic sequence | |
| 650 | 4 | |a convex programming | |
| 650 | 4 | |a hyperspectral compressive sensing | |
| 650 | 4 | |a high spatial correlation | |
| 650 | 4 | |a hyperspectral imaging | |
| 650 | 4 | |a image coding | |
| 650 | 4 | |a Vectors | |
| 650 | 4 | |a signal subspace | |
| 650 | 4 | |a data cube reconstruction | |
| 650 | 4 | |a Coded aperture | |
| 650 | 4 | |a total variation (TV) | |
| 650 | 4 | |a correlation methods | |
| 650 | 4 | |a high correlation components | |
| 650 | 4 | |a compressed sensing | |
| 650 | 4 | |a HYCA technique | |
| 650 | 4 | |a hyperspectral coded aperture | |
| 650 | 4 | |a convex optimization problem | |
| 650 | 4 | |a compressive sensing (CS) | |
| 650 | 4 | |a variation regularizer | |
| 650 | 4 | |a image reconstruction | |
| 650 | 4 | |a Optimization | |
| 650 | 4 | |a Satellites | |
| 650 | 4 | |a Data processing | |
| 700 | 1 | |a Bioucas-Dias, Jose M |4 oth | |
| 700 | 1 | |a Plaza, Antonio |4 oth | |
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10.1109/TGRS.2014.2365534 doi PQ20160617 (DE-627)OLC1965771556 (DE-599)GBVOLC1965771556 (PRQ)c2412-339c281381a5ed80a79850c13fab535fa870620e7ce2be34f03a433cf1390ec40 (KEY)0048677920150000053000502819hycaanewtechniqueforhyperspectralcompressivesensin DE-627 ger DE-627 rakwb eng 620 550 DNB Martin, Gabriel verfasserin aut HYCA: A New Technique for Hyperspectral Compressive Sensing 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Hyperspectral imaging relies on sophisticated acquisition and data processing systems able to acquire, process, store, and transmit hundreds or thousands of image bands from a given area of interest. In this paper, we exploit the high correlation existing among the components of the hyperspectral data sets to introduce a new compressive sensing methodology, termed hyperspectral coded aperture (HYCA), which largely reduces the number of measurements necessary to correctly reconstruct the original data. HYCA relies on two central properties of most hyperspectral images, usually termed data cubes: 1) the spectral vectors live on a low-dimensional subspace; and 2) the spectral bands present high correlation in both the spatial and the spectral domain. The former property allows to represent the data vectors using a small number of coordinates. In this paper, we particularly exploit the high spatial correlation mentioned in the latter property, which implies that each coordinate is piecewise smooth and thus compressible using local differences. The measurement matrix computes a small number of random projections for every spectral vector, which is connected with coded aperture schemes. The reconstruction of the data cube is obtained by solving a convex optimization problem containing a data term linked to the measurement matrix and a total variation regularizer. The solution of this optimization problem is obtained by an instance of the alternating direction method of multipliers that decomposes very hard problems into a cyclic sequence of simpler problems. In order to address the need to set up the parameters involved in the HYCA algorithm, we also develop a constrained version of HYCA (C-HYCA), in which all the parameters can be automatically estimated, which is an important aspect for practical application of the algorithm. A series of experiments with simulated and real data shows the effectiveness of HYCA and C-HYCA, indicating their potential in real-world applications. cyclic sequence convex programming hyperspectral compressive sensing high spatial correlation hyperspectral imaging image coding Vectors signal subspace data cube reconstruction Coded aperture total variation (TV) correlation methods high correlation components compressed sensing HYCA technique hyperspectral coded aperture convex optimization problem compressive sensing (CS) variation regularizer image reconstruction Optimization Satellites Data processing Bioucas-Dias, Jose M oth Plaza, Antonio oth Enthalten in IEEE transactions on geoscience and remote sensing New York, NY : IEEE, 1964 53(2015), 5, Seite 2819-2831 (DE-627)129601667 (DE-600)241439-9 (DE-576)015095282 0196-2892 nnns volume:53 year:2015 number:5 pages:2819-2831 http://dx.doi.org/10.1109/TGRS.2014.2365534 Volltext http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6964803 http://search.proquest.com/docview/1644050726 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-ARC SSG-OLC-TEC SSG-OLC-GEO SSG-OLC-FOR SSG-OPC-GGO SSG-OPC-GEO GBV_ILN_70 GBV_ILN_2027 AR 53 2015 5 2819-2831 |
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10.1109/TGRS.2014.2365534 doi PQ20160617 (DE-627)OLC1965771556 (DE-599)GBVOLC1965771556 (PRQ)c2412-339c281381a5ed80a79850c13fab535fa870620e7ce2be34f03a433cf1390ec40 (KEY)0048677920150000053000502819hycaanewtechniqueforhyperspectralcompressivesensin DE-627 ger DE-627 rakwb eng 620 550 DNB Martin, Gabriel verfasserin aut HYCA: A New Technique for Hyperspectral Compressive Sensing 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Hyperspectral imaging relies on sophisticated acquisition and data processing systems able to acquire, process, store, and transmit hundreds or thousands of image bands from a given area of interest. In this paper, we exploit the high correlation existing among the components of the hyperspectral data sets to introduce a new compressive sensing methodology, termed hyperspectral coded aperture (HYCA), which largely reduces the number of measurements necessary to correctly reconstruct the original data. HYCA relies on two central properties of most hyperspectral images, usually termed data cubes: 1) the spectral vectors live on a low-dimensional subspace; and 2) the spectral bands present high correlation in both the spatial and the spectral domain. The former property allows to represent the data vectors using a small number of coordinates. In this paper, we particularly exploit the high spatial correlation mentioned in the latter property, which implies that each coordinate is piecewise smooth and thus compressible using local differences. The measurement matrix computes a small number of random projections for every spectral vector, which is connected with coded aperture schemes. The reconstruction of the data cube is obtained by solving a convex optimization problem containing a data term linked to the measurement matrix and a total variation regularizer. The solution of this optimization problem is obtained by an instance of the alternating direction method of multipliers that decomposes very hard problems into a cyclic sequence of simpler problems. In order to address the need to set up the parameters involved in the HYCA algorithm, we also develop a constrained version of HYCA (C-HYCA), in which all the parameters can be automatically estimated, which is an important aspect for practical application of the algorithm. A series of experiments with simulated and real data shows the effectiveness of HYCA and C-HYCA, indicating their potential in real-world applications. cyclic sequence convex programming hyperspectral compressive sensing high spatial correlation hyperspectral imaging image coding Vectors signal subspace data cube reconstruction Coded aperture total variation (TV) correlation methods high correlation components compressed sensing HYCA technique hyperspectral coded aperture convex optimization problem compressive sensing (CS) variation regularizer image reconstruction Optimization Satellites Data processing Bioucas-Dias, Jose M oth Plaza, Antonio oth Enthalten in IEEE transactions on geoscience and remote sensing New York, NY : IEEE, 1964 53(2015), 5, Seite 2819-2831 (DE-627)129601667 (DE-600)241439-9 (DE-576)015095282 0196-2892 nnns volume:53 year:2015 number:5 pages:2819-2831 http://dx.doi.org/10.1109/TGRS.2014.2365534 Volltext http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6964803 http://search.proquest.com/docview/1644050726 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-ARC SSG-OLC-TEC SSG-OLC-GEO SSG-OLC-FOR SSG-OPC-GGO SSG-OPC-GEO GBV_ILN_70 GBV_ILN_2027 AR 53 2015 5 2819-2831 |
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10.1109/TGRS.2014.2365534 doi PQ20160617 (DE-627)OLC1965771556 (DE-599)GBVOLC1965771556 (PRQ)c2412-339c281381a5ed80a79850c13fab535fa870620e7ce2be34f03a433cf1390ec40 (KEY)0048677920150000053000502819hycaanewtechniqueforhyperspectralcompressivesensin DE-627 ger DE-627 rakwb eng 620 550 DNB Martin, Gabriel verfasserin aut HYCA: A New Technique for Hyperspectral Compressive Sensing 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Hyperspectral imaging relies on sophisticated acquisition and data processing systems able to acquire, process, store, and transmit hundreds or thousands of image bands from a given area of interest. In this paper, we exploit the high correlation existing among the components of the hyperspectral data sets to introduce a new compressive sensing methodology, termed hyperspectral coded aperture (HYCA), which largely reduces the number of measurements necessary to correctly reconstruct the original data. HYCA relies on two central properties of most hyperspectral images, usually termed data cubes: 1) the spectral vectors live on a low-dimensional subspace; and 2) the spectral bands present high correlation in both the spatial and the spectral domain. The former property allows to represent the data vectors using a small number of coordinates. In this paper, we particularly exploit the high spatial correlation mentioned in the latter property, which implies that each coordinate is piecewise smooth and thus compressible using local differences. The measurement matrix computes a small number of random projections for every spectral vector, which is connected with coded aperture schemes. The reconstruction of the data cube is obtained by solving a convex optimization problem containing a data term linked to the measurement matrix and a total variation regularizer. The solution of this optimization problem is obtained by an instance of the alternating direction method of multipliers that decomposes very hard problems into a cyclic sequence of simpler problems. In order to address the need to set up the parameters involved in the HYCA algorithm, we also develop a constrained version of HYCA (C-HYCA), in which all the parameters can be automatically estimated, which is an important aspect for practical application of the algorithm. A series of experiments with simulated and real data shows the effectiveness of HYCA and C-HYCA, indicating their potential in real-world applications. cyclic sequence convex programming hyperspectral compressive sensing high spatial correlation hyperspectral imaging image coding Vectors signal subspace data cube reconstruction Coded aperture total variation (TV) correlation methods high correlation components compressed sensing HYCA technique hyperspectral coded aperture convex optimization problem compressive sensing (CS) variation regularizer image reconstruction Optimization Satellites Data processing Bioucas-Dias, Jose M oth Plaza, Antonio oth Enthalten in IEEE transactions on geoscience and remote sensing New York, NY : IEEE, 1964 53(2015), 5, Seite 2819-2831 (DE-627)129601667 (DE-600)241439-9 (DE-576)015095282 0196-2892 nnns volume:53 year:2015 number:5 pages:2819-2831 http://dx.doi.org/10.1109/TGRS.2014.2365534 Volltext http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6964803 http://search.proquest.com/docview/1644050726 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-ARC SSG-OLC-TEC SSG-OLC-GEO SSG-OLC-FOR SSG-OPC-GGO SSG-OPC-GEO GBV_ILN_70 GBV_ILN_2027 AR 53 2015 5 2819-2831 |
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10.1109/TGRS.2014.2365534 doi PQ20160617 (DE-627)OLC1965771556 (DE-599)GBVOLC1965771556 (PRQ)c2412-339c281381a5ed80a79850c13fab535fa870620e7ce2be34f03a433cf1390ec40 (KEY)0048677920150000053000502819hycaanewtechniqueforhyperspectralcompressivesensin DE-627 ger DE-627 rakwb eng 620 550 DNB Martin, Gabriel verfasserin aut HYCA: A New Technique for Hyperspectral Compressive Sensing 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Hyperspectral imaging relies on sophisticated acquisition and data processing systems able to acquire, process, store, and transmit hundreds or thousands of image bands from a given area of interest. In this paper, we exploit the high correlation existing among the components of the hyperspectral data sets to introduce a new compressive sensing methodology, termed hyperspectral coded aperture (HYCA), which largely reduces the number of measurements necessary to correctly reconstruct the original data. HYCA relies on two central properties of most hyperspectral images, usually termed data cubes: 1) the spectral vectors live on a low-dimensional subspace; and 2) the spectral bands present high correlation in both the spatial and the spectral domain. The former property allows to represent the data vectors using a small number of coordinates. In this paper, we particularly exploit the high spatial correlation mentioned in the latter property, which implies that each coordinate is piecewise smooth and thus compressible using local differences. The measurement matrix computes a small number of random projections for every spectral vector, which is connected with coded aperture schemes. The reconstruction of the data cube is obtained by solving a convex optimization problem containing a data term linked to the measurement matrix and a total variation regularizer. The solution of this optimization problem is obtained by an instance of the alternating direction method of multipliers that decomposes very hard problems into a cyclic sequence of simpler problems. In order to address the need to set up the parameters involved in the HYCA algorithm, we also develop a constrained version of HYCA (C-HYCA), in which all the parameters can be automatically estimated, which is an important aspect for practical application of the algorithm. A series of experiments with simulated and real data shows the effectiveness of HYCA and C-HYCA, indicating their potential in real-world applications. cyclic sequence convex programming hyperspectral compressive sensing high spatial correlation hyperspectral imaging image coding Vectors signal subspace data cube reconstruction Coded aperture total variation (TV) correlation methods high correlation components compressed sensing HYCA technique hyperspectral coded aperture convex optimization problem compressive sensing (CS) variation regularizer image reconstruction Optimization Satellites Data processing Bioucas-Dias, Jose M oth Plaza, Antonio oth Enthalten in IEEE transactions on geoscience and remote sensing New York, NY : IEEE, 1964 53(2015), 5, Seite 2819-2831 (DE-627)129601667 (DE-600)241439-9 (DE-576)015095282 0196-2892 nnns volume:53 year:2015 number:5 pages:2819-2831 http://dx.doi.org/10.1109/TGRS.2014.2365534 Volltext http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6964803 http://search.proquest.com/docview/1644050726 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-ARC SSG-OLC-TEC SSG-OLC-GEO SSG-OLC-FOR SSG-OPC-GGO SSG-OPC-GEO GBV_ILN_70 GBV_ILN_2027 AR 53 2015 5 2819-2831 |
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10.1109/TGRS.2014.2365534 doi PQ20160617 (DE-627)OLC1965771556 (DE-599)GBVOLC1965771556 (PRQ)c2412-339c281381a5ed80a79850c13fab535fa870620e7ce2be34f03a433cf1390ec40 (KEY)0048677920150000053000502819hycaanewtechniqueforhyperspectralcompressivesensin DE-627 ger DE-627 rakwb eng 620 550 DNB Martin, Gabriel verfasserin aut HYCA: A New Technique for Hyperspectral Compressive Sensing 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Hyperspectral imaging relies on sophisticated acquisition and data processing systems able to acquire, process, store, and transmit hundreds or thousands of image bands from a given area of interest. In this paper, we exploit the high correlation existing among the components of the hyperspectral data sets to introduce a new compressive sensing methodology, termed hyperspectral coded aperture (HYCA), which largely reduces the number of measurements necessary to correctly reconstruct the original data. HYCA relies on two central properties of most hyperspectral images, usually termed data cubes: 1) the spectral vectors live on a low-dimensional subspace; and 2) the spectral bands present high correlation in both the spatial and the spectral domain. The former property allows to represent the data vectors using a small number of coordinates. In this paper, we particularly exploit the high spatial correlation mentioned in the latter property, which implies that each coordinate is piecewise smooth and thus compressible using local differences. The measurement matrix computes a small number of random projections for every spectral vector, which is connected with coded aperture schemes. The reconstruction of the data cube is obtained by solving a convex optimization problem containing a data term linked to the measurement matrix and a total variation regularizer. The solution of this optimization problem is obtained by an instance of the alternating direction method of multipliers that decomposes very hard problems into a cyclic sequence of simpler problems. In order to address the need to set up the parameters involved in the HYCA algorithm, we also develop a constrained version of HYCA (C-HYCA), in which all the parameters can be automatically estimated, which is an important aspect for practical application of the algorithm. A series of experiments with simulated and real data shows the effectiveness of HYCA and C-HYCA, indicating their potential in real-world applications. cyclic sequence convex programming hyperspectral compressive sensing high spatial correlation hyperspectral imaging image coding Vectors signal subspace data cube reconstruction Coded aperture total variation (TV) correlation methods high correlation components compressed sensing HYCA technique hyperspectral coded aperture convex optimization problem compressive sensing (CS) variation regularizer image reconstruction Optimization Satellites Data processing Bioucas-Dias, Jose M oth Plaza, Antonio oth Enthalten in IEEE transactions on geoscience and remote sensing New York, NY : IEEE, 1964 53(2015), 5, Seite 2819-2831 (DE-627)129601667 (DE-600)241439-9 (DE-576)015095282 0196-2892 nnns volume:53 year:2015 number:5 pages:2819-2831 http://dx.doi.org/10.1109/TGRS.2014.2365534 Volltext http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6964803 http://search.proquest.com/docview/1644050726 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-ARC SSG-OLC-TEC SSG-OLC-GEO SSG-OLC-FOR SSG-OPC-GGO SSG-OPC-GEO GBV_ILN_70 GBV_ILN_2027 AR 53 2015 5 2819-2831 |
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Martin, Gabriel ddc 620 misc cyclic sequence misc convex programming misc hyperspectral compressive sensing misc high spatial correlation misc hyperspectral imaging misc image coding misc Vectors misc signal subspace misc data cube reconstruction misc Coded aperture misc total variation (TV) misc correlation methods misc high correlation components misc compressed sensing misc HYCA technique misc hyperspectral coded aperture misc convex optimization problem misc compressive sensing (CS) misc variation regularizer misc image reconstruction misc Optimization misc Satellites misc Data processing HYCA: A New Technique for Hyperspectral Compressive Sensing |
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620 550 DNB HYCA: A New Technique for Hyperspectral Compressive Sensing cyclic sequence convex programming hyperspectral compressive sensing high spatial correlation hyperspectral imaging image coding Vectors signal subspace data cube reconstruction Coded aperture total variation (TV) correlation methods high correlation components compressed sensing HYCA technique hyperspectral coded aperture convex optimization problem compressive sensing (CS) variation regularizer image reconstruction Optimization Satellites Data processing |
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HYCA: A New Technique for Hyperspectral Compressive Sensing |
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Hyperspectral imaging relies on sophisticated acquisition and data processing systems able to acquire, process, store, and transmit hundreds or thousands of image bands from a given area of interest. In this paper, we exploit the high correlation existing among the components of the hyperspectral data sets to introduce a new compressive sensing methodology, termed hyperspectral coded aperture (HYCA), which largely reduces the number of measurements necessary to correctly reconstruct the original data. HYCA relies on two central properties of most hyperspectral images, usually termed data cubes: 1) the spectral vectors live on a low-dimensional subspace; and 2) the spectral bands present high correlation in both the spatial and the spectral domain. The former property allows to represent the data vectors using a small number of coordinates. In this paper, we particularly exploit the high spatial correlation mentioned in the latter property, which implies that each coordinate is piecewise smooth and thus compressible using local differences. The measurement matrix computes a small number of random projections for every spectral vector, which is connected with coded aperture schemes. The reconstruction of the data cube is obtained by solving a convex optimization problem containing a data term linked to the measurement matrix and a total variation regularizer. The solution of this optimization problem is obtained by an instance of the alternating direction method of multipliers that decomposes very hard problems into a cyclic sequence of simpler problems. In order to address the need to set up the parameters involved in the HYCA algorithm, we also develop a constrained version of HYCA (C-HYCA), in which all the parameters can be automatically estimated, which is an important aspect for practical application of the algorithm. A series of experiments with simulated and real data shows the effectiveness of HYCA and C-HYCA, indicating their potential in real-world applications. |
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Hyperspectral imaging relies on sophisticated acquisition and data processing systems able to acquire, process, store, and transmit hundreds or thousands of image bands from a given area of interest. In this paper, we exploit the high correlation existing among the components of the hyperspectral data sets to introduce a new compressive sensing methodology, termed hyperspectral coded aperture (HYCA), which largely reduces the number of measurements necessary to correctly reconstruct the original data. HYCA relies on two central properties of most hyperspectral images, usually termed data cubes: 1) the spectral vectors live on a low-dimensional subspace; and 2) the spectral bands present high correlation in both the spatial and the spectral domain. The former property allows to represent the data vectors using a small number of coordinates. In this paper, we particularly exploit the high spatial correlation mentioned in the latter property, which implies that each coordinate is piecewise smooth and thus compressible using local differences. The measurement matrix computes a small number of random projections for every spectral vector, which is connected with coded aperture schemes. The reconstruction of the data cube is obtained by solving a convex optimization problem containing a data term linked to the measurement matrix and a total variation regularizer. The solution of this optimization problem is obtained by an instance of the alternating direction method of multipliers that decomposes very hard problems into a cyclic sequence of simpler problems. In order to address the need to set up the parameters involved in the HYCA algorithm, we also develop a constrained version of HYCA (C-HYCA), in which all the parameters can be automatically estimated, which is an important aspect for practical application of the algorithm. A series of experiments with simulated and real data shows the effectiveness of HYCA and C-HYCA, indicating their potential in real-world applications. |
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Hyperspectral imaging relies on sophisticated acquisition and data processing systems able to acquire, process, store, and transmit hundreds or thousands of image bands from a given area of interest. In this paper, we exploit the high correlation existing among the components of the hyperspectral data sets to introduce a new compressive sensing methodology, termed hyperspectral coded aperture (HYCA), which largely reduces the number of measurements necessary to correctly reconstruct the original data. HYCA relies on two central properties of most hyperspectral images, usually termed data cubes: 1) the spectral vectors live on a low-dimensional subspace; and 2) the spectral bands present high correlation in both the spatial and the spectral domain. The former property allows to represent the data vectors using a small number of coordinates. In this paper, we particularly exploit the high spatial correlation mentioned in the latter property, which implies that each coordinate is piecewise smooth and thus compressible using local differences. The measurement matrix computes a small number of random projections for every spectral vector, which is connected with coded aperture schemes. The reconstruction of the data cube is obtained by solving a convex optimization problem containing a data term linked to the measurement matrix and a total variation regularizer. The solution of this optimization problem is obtained by an instance of the alternating direction method of multipliers that decomposes very hard problems into a cyclic sequence of simpler problems. In order to address the need to set up the parameters involved in the HYCA algorithm, we also develop a constrained version of HYCA (C-HYCA), in which all the parameters can be automatically estimated, which is an important aspect for practical application of the algorithm. A series of experiments with simulated and real data shows the effectiveness of HYCA and C-HYCA, indicating their potential in real-world applications. |
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