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## Sparse unmixing of hyperspectral data (2011)

Venue: | IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING |

Citations: | 51 - 15 self |

### Citations

2717 | Atomic Decomposition by Basis Pursuit
- Chen, Donoho, et al.
- 1998
(Show Context)
Citation Context ...], and therefore, there is a little hope in solving it in a straightforward way. Greedy algorithms such as the orthogonal basis pursuit [orthogonal matching pursuit (OMP)] [33] and basis pursuit (BP) =-=[34]-=- are two alternative approaches in computing the sparsest solution. BP replaces the ℓ0 norm in (P0) with the ℓ1 norm (P1) : (7) min x ‖x‖1 subject to Ax = y. (8)2018 IEEE TRANSACTIONS ON GEOSCIENCE A... |

1398 | Decoding by linear programming
- Candès, Tao
(Show Context)
Citation Context ... unexpected is that, in given circumstances related to matrix A, problem (P1) has the same solution as problem (P0). This result is stated in terms of the restricted isometric constants introduced in =-=[27]-=-. Herein, we use the variant proposed in [35]. Let αk, with βk ≥ 0, be the tightest constants in the inequalities and further define αk‖x‖2 ≤‖Ax‖2 ≤ βk‖x‖2, ‖x‖0 ≤ k (9) γ2s ≡ β2 2s α2 ≥ 1. (10) 2s Th... |

1389 | Stable signal recovery from incomplete and inaccurate measurements
- Candès, Romberg, et al.
(Show Context)
Citation Context ...rmined system of equations mostly depends on the degree of coherence between the columns of the system matrix and the degree of sparseness of the original signals (i.e., the abundance fractions) [25]–=-=[28]-=-. The most favorable scenarios correspond to highly sparse signals and system matrices with low coherence. Unfortunately, in hyperspectral applications, the spectral signatures of the materials tend t... |

797 | Signal recovery from random measurements via orthogonal matching pursuit
- Tropp, Gilbert
(Show Context)
Citation Context ... shown that, in some cases, the OMP algorithm also provides the (P0) solution in a fashion that is comparable with the BP alternative, with the advantage of being faster and easier to implement [26], =-=[36]-=-. 2) Nonnegative Signals: We now consider the problem ( ) + P 0 : min‖x‖0subject to Ax = y x ≥ 0 (11) x and follow a line of reasoning that is close to that of [25]. The hyperspectral libraries genera... |

632 | Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition
- Pati, Rezaiifar, et al.
- 1993
(Show Context)
Citation Context ...d very complex to solve) [32], and therefore, there is a little hope in solving it in a straightforward way. Greedy algorithms such as the orthogonal basis pursuit [orthogonal matching pursuit (OMP)] =-=[33]-=- and basis pursuit (BP) [34] are two alternative approaches in computing the sparsest solution. BP replaces the ℓ0 norm in (P0) with the ℓ1 norm (P1) : (7) min x ‖x‖1 subject to Ax = y. (8)2018 IEEE ... |

630 | Optimally sparse representation in general (nonorthogonal) dictionaries via l-minimization
- Donoho, Elad
- 2003
(Show Context)
Citation Context ...f linear equations Ax = y has a solution satisfying 2‖x‖0 < spark(A), where spark(A) ≤ rank(A)+1 is the smallest number of linearly dependent columns of A,itis necessarily the unique solution of (P0) =-=[30]-=-, [31]. The spark of a matrix gives us a very simple way to check the uniqueness of a solution of the system Ax = y. For example, if the elements of A are independent and identically distributed (i.i.... |

556 |
Sparse approximate solutions to linear systems
- Natarajan
- 1995
(Show Context)
Citation Context ...strategies for computing (P0): pursuit algorithms and nonnegative signals. 1) Pursuit Algorithms: The problem (P0) is NP hard (which means that the problem is combinatorial and very complex to solve) =-=[32]-=-, and therefore, there is a little hope in solving it in a straightforward way. Greedy algorithms such as the orthogonal basis pursuit [orthogonal matching pursuit (OMP)] [33] and basis pursuit (BP) [... |

460 | Stable recovery of sparse overcomplete representations in the presence of noise
- Donoho, Elad, et al.
- 2006
(Show Context)
Citation Context ...oise-tolerant SR optimization problem is then ( ) δ P0 : min‖x‖0subject to ‖Ax − y‖2 ≤ δ. (16) x The concept of uniqueness of the sparsest solution is now replaced with the concept of stability [35], =-=[38]-=-, [39]. For example, in [38], it is shown that, given a sparse vector x0 satisfying the sparsity constraint x0 < (1 + 1/μ(A))/2 such that ‖Ax0 − y‖ ≤δ, then every solution x δ 0 of problem (P δ 0 ) sa... |

425 | From sparse solutions of systems of equations to sparse modeling of signals and images - Bruckstein, Donoho, et al. - 2009 |

388 | On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators
- Eckstein, Bertsekas
- 1992
(Show Context)
Citation Context .... CSUnSAL is tailored to hyperspectral applications with hundreds of thousands or millions of spectral vectors to unmix. This algorithm exploits the alternating direction method of multipliers (ADMM) =-=[40]-=- in a way that is similar to recent works [41], [42]. Here, we use the acronyms CSUnSAL, CSUnSAL + , CSUnSAL δ , and CSUnSAL δ+ to denote the variant of CSUnSAL tailored to (P1), (P + 1 ), (P δ 1 ), a... |

366 | Sparse signal reconstruction from limited data using focuss: a re-weighted minimum norm algorithm
- Gorodnitsky, Rao
- 1997
(Show Context)
Citation Context ...ar equations Ax = y has a solution satisfying 2‖x‖0 < spark(A), where spark(A) ≤ rank(A)+1 is the smallest number of linearly dependent columns of A,itis necessarily the unique solution of (P0) [30], =-=[31]-=-. The spark of a matrix gives us a very simple way to check the uniqueness of a solution of the system Ax = y. For example, if the elements of A are independent and identically distributed (i.i.d.), t... |

221 |
A survey of spectral unmixing
- Keshava
- 2003
(Show Context)
Citation Context ...ed into a linear combination of pure spectral signatures of soil and vegetation, weighted by abundance fractions that indicate the proportion of each macroscopically pure signature in the mixed pixel =-=[5]-=-. To deal with this problem, linear spectral mixture analysis techniques first identify a collection of spectrally pure constituent spectra, called as endmembers in the literature, and then express th... |

192 | Bioucas-Dias, “Vertex component analysis: a fast algorithm to unmix hyperspectral data
- Nascimento, M
- 2005
(Show Context)
Citation Context ...working under this regime, we can list some popular approaches such as the pixel purity index [11], N-FINDR [12], orthogonal subspace projection technique in [13], and vertex component analysis (VCA) =-=[14]-=-. However, the assumption under which these algorithms perform may be difficult to guarantee in practical applications due to several reasons. 1) First, if the spatial resolution of the sensor is not ... |

192 | Sparsest solutions of underdetermined linear systems via ℓq-minimization for 0 < q ≤ 1
- Foucart, Lai
(Show Context)
Citation Context ...elated to matrix A, problem (P1) has the same solution as problem (P0). This result is stated in terms of the restricted isometric constants introduced in [27]. Herein, we use the variant proposed in =-=[35]-=-. Let αk, with βk ≥ 0, be the tightest constants in the inequalities and further define αk‖x‖2 ≤‖Ax‖2 ≤ βk‖x‖2, ‖x‖0 ≤ k (9) γ2s ≡ β2 2s α2 ≥ 1. (10) 2s Then, under the assumption that γ2s < 4 √ 2 − 3... |

182 |
Mapping target signatures via partial unmixing of AVIRIS data,”
- Boardman, Kruse, et al.
- 1995
(Show Context)
Citation Context ...most spectrally pure signatures in the input scene is feasible. Among the endmember extraction algorithms working under this regime, we can list some popular approaches such as the pixel purity index =-=[11]-=-, N-FINDR [12], orthogonal subspace projection technique in [13], and vertex component analysis (VCA) [14]. However, the assumption under which these algorithms perform may be difficult to guarantee i... |

180 |
Signal Theory Methods in Multispectral Remote Sensing,
- Landgrebe
- 2003
(Show Context)
Citation Context ...ical tools have been developed for remotely sensed hyperspectral data processing in recent years, covering topics like dimensionality reduction, classification, data compression, or spectral unmixing =-=[3]-=-, [4]. The underlying assumption governing clustering and classification techniques is that each pixel vector comprises the response of a single underlying material. However, if the spatial resolution... |

177 |
N-finder: an algorithm for fast autonomous spectral endmember determination in hyperspectral data,” Image Spectrometry V,
- Winter
- 1999
(Show Context)
Citation Context ...y pure signatures in the input scene is feasible. Among the endmember extraction algorithms working under this regime, we can list some popular approaches such as the pixel purity index [11], N-FINDR =-=[12]-=-, orthogonal subspace projection technique in [13], and vertex component analysis (VCA) [14]. However, the assumption under which these algorithms perform may be difficult to guarantee in practical ap... |

176 |
Hyperspectral Imaging: Techniques for Spectral Detection and Classification
- CHANG
- 2003
(Show Context)
Citation Context ...tools have been developed for remotely sensed hyperspectral data processing in recent years, covering topics like dimensionality reduction, classification, data compression, or spectral unmixing [3], =-=[4]-=-. The underlying assumption governing clustering and classification techniques is that each pixel vector comprises the response of a single underlying material. However, if the spatial resolution of t... |

172 |
Spectral Mixture Modeling: A New Analysis of Rock and Soil Types at the Viking Lander 1
- Adams, Smith, et al.
- 1986
(Show Context)
Citation Context ...nd then express the measured spectrum of each mixed pixel as a linear combination of endmembers weighted by fractions or abundances that indicate the proportion of each endmember present in the pixel =-=[6]-=-. It should be noted that the linear mixture model assumes minimal secondary reflections and/or multiple scattering effects in the data collection procedure, and hence, the measured spectra can be exp... |

168 | Fully constrained least squares linear spectral mixture analysis method for material quantification in hyperspectral imagery
- Heinz, Chang
- 2001
(Show Context)
Citation Context ...ASC) ( ∑q i=1 αi =1), which we, respectively, represent in compact form by α ≥ 0 (3) 1 T α =1 (4) where 1 T is a line vector of 1’s compatible with α, areoften imposed into the model described in (1) =-=[7]-=-, owing to the fact that αi, fori =1,...,q, represents the fractions of the endmembers present in the considered pixel. In a typical hyperspectral unmixing scenario, we are given a set Y ≡{yi ∈ R L ,i... |

131 |
Imaging spectrometry for earth remote sensing,
- Goetz, Vane, et al.
- 1985
(Show Context)
Citation Context ... Identifier 10.1109/TGRS.2010.2098413 I. INTRODUCTION HYPERSPECTRAL imaging has been transformed from being a sparse research tool into a commodity product that is available to a broad user community =-=[1]-=-. The wealth of spectral information available from advanced hyperspectral imaging instruments currently in operation has opened new perspectives in many application domains, such as monitoring of env... |

109 |
Imaging Spectroscopy and the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS). Remote Sens.
- Green, Eastwood, et al.
- 1998
(Show Context)
Citation Context ...ting biological threats, and monitoring oil spills and other types of chemical contamination. Advanced hyperspectral instruments such as NASA’s Airborne Visible Infrared Imaging Spectrometer (AVIRIS) =-=[2]-=- are now able to cover the wavelength region from 0.4 to 2.5 μm using more than 200 spectral channels at a nominal spectral resolution of 10 nm. The resulting hyperspectral data cube is a stack of ima... |

104 |
A quantitative and comparative analysis of endmember extraction algorithms from hyperspectral data
- Plaza, Martinez, et al.
- 2004
(Show Context)
Citation Context ...whose vertices are the columns of M. Overthe last decade, several algorithms have exploited this geometrical property by estimating the “smallest” simplex set containing the observed spectral vectors =-=[9]-=-, [10]. Some classic techniques for this purpose assume that the input data set contains at least one pure pixel for each distinct material present in the scene, and therefore, a search procedure aime... |

103 | Spatial/spectral endmember extraction by multidimensional morphological operations
- Plaza, Martinez, et al.
- 2002
(Show Context)
Citation Context ...t data. Such techniques include optical real-time adaptive spectral identification systems [15], convex cone analysis [16], iterative error analysis [17], automatic morphological endmember extraction =-=[18]-=-, iterated constrained endmembers (ICE) [19], minimum volume constrained nonnegative matrix factorization [20], spatial–spectral endmember extraction [21], sparsity-promoting ICE [22], minimum volume ... |

103 | Just relax : Convex programming methods for subset selection and sparse approximation,”
- Tropp
- 2006
(Show Context)
Citation Context ...olerant SR optimization problem is then ( ) δ P0 : min‖x‖0subject to ‖Ax − y‖2 ≤ δ. (16) x The concept of uniqueness of the sparsest solution is now replaced with the concept of stability [35], [38], =-=[39]-=-. For example, in [38], it is shown that, given a sparse vector x0 satisfying the sparsity constraint x0 < (1 + 1/μ(A))/2 such that ‖Ax0 − y‖ ≤δ, then every solution x δ 0 of problem (P δ 0 ) satisfie... |

87 |
Endmember extraction from highly mixed data using minimum volume constrained nonnegative matrix factorization
- Miao, Qi
- 2007
(Show Context)
Citation Context ...nalysis [16], iterative error analysis [17], automatic morphological endmember extraction [18], iterated constrained endmembers (ICE) [19], minimum volume constrained nonnegative matrix factorization =-=[20]-=-, spatial–spectral endmember extraction [21], sparsity-promoting ICE [22], minimum volume simplex analysis [23], and simplex identification via split augmented Lagrangian [24]. A necessary condition f... |

84 |
Imaging spectroscopy: Earth and planetary remote sensing with the usgs tetracorder and expert systems,”
- Clark, Swayze, et al.
- 2003
(Show Context)
Citation Context ...his library as the input to the unmixing methods described in Section III. For illustrative purposes, Fig. 15 shows a mineral map produced in 1995 by USGS, in which the Tricorder 3.3 software product =-=[46]-=- was used to map different minerals present in the Cuprite mining district. 8 It should be noted that the Tricorder map is only available for the hyperspectral data collected in 1995, while the public... |

83 | Hyperspectral subspace identification,"
- Bioucas-Dias, Nascimento
- 2008
(Show Context)
Citation Context ...s in the Cuprite mining district in NV. The map is available online at http://speclab.cr.usgs.gov/cuprite95.tgif.2.2um_map.gif. Once the simulated data set was generated, we used the HySime algorithm =-=[45]-=- to find the signal subspace and projected the data on this subspace. Then, two endmember extraction algorithms (VCA and N-FINDR) were used to automatically extract the endmembers from the simulated d... |

61 | Does independent component analysis play a role in unmixing hyperspectral data?”
- Nascimento, Bioucas-Dias
- 2005
(Show Context)
Citation Context ...bundances associated to each pixel is constant. Thus, the sources are statistically dependent, which compromises the performance of independent component analysis algorithms in hyperspectral unmixing =-=[8]-=-.2016 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 49, NO. 6, JUNE 2011 We note that the constraints (3) and (4) define the set Sq−1 ≡ {α ∈ Rq |α ≥ 0, 1T α =1}, which is the probability s... |

55 | Minimum volume simplex analysis: A fast algorithm to unmix hyperspectral data,” in Proc
- Li, Bioucas-Dias
- 2008
(Show Context)
Citation Context ...ained endmembers (ICE) [19], minimum volume constrained nonnegative matrix factorization [20], spatial–spectral endmember extraction [21], sparsity-promoting ICE [22], minimum volume simplex analysis =-=[23]-=-, and simplex identification via split augmented Lagrangian [24]. A necessary condition for these endmember generation techniques to yield good estimates is the presence in the data set of at least q ... |

52 |
Automatic endmember extraction from hyperspectral data for mineral exploration
- Neville, Staenz, et al.
- 1999
(Show Context)
Citation Context ...on that pure signatures are not present in the input data. Such techniques include optical real-time adaptive spectral identification systems [15], convex cone analysis [16], iterative error analysis =-=[17]-=-, automatic morphological endmember extraction [18], iterated constrained endmembers (ICE) [19], minimum volume constrained nonnegative matrix factorization [20], spatial–spectral endmember extraction... |

46 | ICE: A statistical approach to identifying endmembers in hyperspectral images,”
- Berman, Kiiveri, et al.
- 2004
(Show Context)
Citation Context ...-time adaptive spectral identification systems [15], convex cone analysis [16], iterative error analysis [17], automatic morphological endmember extraction [18], iterated constrained endmembers (ICE) =-=[19]-=-, minimum volume constrained nonnegative matrix factorization [20], spatial–spectral endmember extraction [21], sparsity-promoting ICE [22], minimum volume simplex analysis [23], and simplex identific... |

44 | On the uniqueness of nonnegative sparse solutions to underdetermined systems of equations
- Bruckstein, Elad, et al.
- 2008
(Show Context)
Citation Context ...rdetermined system of equations mostly depends on the degree of coherence between the columns of the system matrix and the degree of sparseness of the original signals (i.e., the abundance fractions) =-=[25]-=-–[28]. The most favorable scenarios correspond to highly sparse signals and system matrices with low coherence. Unfortunately, in hyperspectral applications, the spectral signatures of the materials t... |

43 |
Automatic spectral target recognition in hyperspectral imagery,"
- Ren, Chang
- 2003
(Show Context)
Citation Context ...Among the endmember extraction algorithms working under this regime, we can list some popular approaches such as the pixel purity index [11], N-FINDR [12], orthogonal subspace projection technique in =-=[13]-=-, and vertex component analysis (VCA) [14]. However, the assumption under which these algorithms perform may be difficult to guarantee in practical applications due to several reasons. 1) First, if th... |

43 | Multispectral and hyperspectral image analysis with convex cones
- Ifarraguerri, Chang
- 1999
(Show Context)
Citation Context ...een proposed under the assumption that pure signatures are not present in the input data. Such techniques include optical real-time adaptive spectral identification systems [15], convex cone analysis =-=[16]-=-, iterative error analysis [17], automatic morphological endmember extraction [18], iterated constrained endmembers (ICE) [19], minimum volume constrained nonnegative matrix factorization [20], spatia... |

41 | A variable splitting augmented lagrangian approach to linear spectral unmixing
- Bioucas-Dias
(Show Context)
Citation Context ...ive matrix factorization [20], spatial–spectral endmember extraction [21], sparsity-promoting ICE [22], minimum volume simplex analysis [23], and simplex identification via split augmented Lagrangian =-=[24]-=-. A necessary condition for these endmember generation techniques to yield good estimates is the presence in the data set of at least q − 1 spectral vectors on each facet of the simplex set SM [24]. T... |

39 |
Endmember bundles: A new approach to incorporating endmember variability into spectral mixture analysis
- Bateson, Asner, et al.
- 2000
(Show Context)
Citation Context ...onnections with the ASC constraint which is so popular in hyperspectral applications. The ASC is, however, prone to strong criticisms because, in a real image, there is a strong signature variability =-=[37]-=- that, at the very least, introduces positive scaling factors varying from pixel to pixel in the signatures present in the mixtures. As a result, the signatures are defined up to a scale factor, and t... |

32 | Alternating direction algorithms for constrained sparse regression: Application to hyperspectral unmixing
- Bioucas-Dias, Figueiredo
- 2010
(Show Context)
Citation Context ...nt optimizations to unmix the complete scene. To cope up with this computational complexity, we resort to recently introduced (fast) algorithms based on the augmented Lagrangian method of multipliers =-=[29]-=-. 1 Available online at http://speclab.cr.usgs.gov/spectral-lib.html. 2 Available online at http://speclib.jpl.nasa.gov.IORDACHE et al.: SPARSE UNMIXING OF HYPERSPECTRAL DATA 2017 In this paper, we s... |

30 |
L1 unmixing and its application to hyperspectral image enhancement
- Guo, Wittman, et al.
(Show Context)
Citation Context ...r, and λ → 0 when δ → 0. This model, sometimes referred to as the least squares (LS) ℓ1 model, is widely used in the signal processing community. It was used before to address the unmixing problem in =-=[43]-=-, in which the endmembers were first extracted from the original image using the N-FINDR endmember extraction algorithm [12], and then, the respective fractional abundances of the endmembers were infe... |

26 |
Sparsity promoting iterated constrained endmember detection for hyperspectral imagery,”
- Zare, Gader
- 2007
(Show Context)
Citation Context ...ember extraction [18], iterated constrained endmembers (ICE) [19], minimum volume constrained nonnegative matrix factorization [20], spatial–spectral endmember extraction [21], sparsity-promoting ICE =-=[22]-=-, minimum volume simplex analysis [23], and simplex identification via split augmented Lagrangian [24]. A necessary condition for these endmember generation techniques to yield good estimates is the p... |

23 |
Iterative spectral unmixing for optimizing per-pixel endmember sets.
- Rogge, Rivard, et al.
- 2006
(Show Context)
Citation Context ...ained versions of the LS problem because, as mentioned before, they are particular cases of (24) when λ =0. D. ISMA In this paper, we also use the iterative spectral mixture analysis (ISMA) algorithm =-=[44]-=- to solve the considered problems. The pseudocode of the ISMA is shown in Algorithm 2. The ISMA is an iterative technique derived from the standard spectral mixture analysis formulation presented in (... |

21 |
Impact of initialization on design of endmember extraction algorithm
- Plaza, Chang
- 2006
(Show Context)
Citation Context ... vertices are the columns of M. Overthe last decade, several algorithms have exploited this geometrical property by estimating the “smallest” simplex set containing the observed spectral vectors [9], =-=[10]-=-. Some classic techniques for this purpose assume that the input data set contains at least one pure pixel for each distinct material present in the scene, and therefore, a search procedure aimed at f... |

21 |
Integration of SpatialSpectral Information for the Improved Extraction of Endmembers.” Remote Sensing of Environment 110:
- Rogge, Rivard, et al.
- 2007
(Show Context)
Citation Context ... automatic morphological endmember extraction [18], iterated constrained endmembers (ICE) [19], minimum volume constrained nonnegative matrix factorization [20], spatial–spectral endmember extraction =-=[21]-=-, sparsity-promoting ICE [22], minimum volume simplex analysis [23], and simplex identification via split augmented Lagrangian [24]. A necessary condition for these endmember generation techniques to ... |

20 |
Use of filter vectors in hyperspectral data analysis
- Bowles, Palmadesso, et al.
- 1995
(Show Context)
Citation Context ...tion algorithms have also been proposed under the assumption that pure signatures are not present in the input data. Such techniques include optical real-time adaptive spectral identification systems =-=[15]-=-, convex cone analysis [16], iterative error analysis [17], automatic morphological endmember extraction [18], iterated constrained endmembers (ICE) [19], minimum volume constrained nonnegative matrix... |

14 | A fast algorithm for the constrained formulation of compressive image reconstruction and other linear inverse problems,” Submitted, Available at http://arxiv.org/abs/0909.3947v1
- Afonso, Bioucas-Dias, et al.
- 2009
(Show Context)
Citation Context ...with hundreds of thousands or millions of spectral vectors to unmix. This algorithm exploits the alternating direction method of multipliers (ADMM) [40] in a way that is similar to recent works [41], =-=[42]-=-. Here, we use the acronyms CSUnSAL, CSUnSAL + , CSUnSAL δ , and CSUnSAL δ+ to denote the variant of CSUnSAL tailored to (P1), (P + 1 ), (P δ 1 ), and (P δ+ 1 ) problems, respectively. C. Unconstraine... |

12 | Fast frame-based image deconvolution using variable splitting and constrained optimization
- Figueiredo, Bioucas-Dias, et al.
- 2009
(Show Context)
Citation Context ...tions with hundreds of thousands or millions of spectral vectors to unmix. This algorithm exploits the alternating direction method of multipliers (ADMM) [40] in a way that is similar to recent works =-=[41]-=-, [42]. Here, we use the acronyms CSUnSAL, CSUnSAL + , CSUnSAL δ , and CSUnSAL δ+ to denote the variant of CSUnSAL tailored to (P1), (P + 1 ), (P δ 1 ), and (P δ+ 1 ) problems, respectively. C. Uncons... |