L1 unmixing and its application to hyperspectral image enhancement

Guo, Zhaohui; Wittman, Todd; Osher, Stanley

doi:10.1117/12.818245

Cited by 112 publications

(98 citation statements)

References 16 publications

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“…Total variation (TV) has been widely used to explore the spatial piecewise smooth structure for tackling various HSI processing tasks [15,28,29]. It has the ability of preserving local spatial consistency and suppressing observed noise.…”

Section: Tv Regularizationmentioning

confidence: 99%

“…In [2], Akgun et al proposed a novel hyperspectral image acquisition model, with which a projection onto convex sets based super-resolution method was proposed to enhance the resolution of HSIs. Guo et al [15] used the unmixing information and total variation (TV) minimization to produce a higher resolution HSI. By modeling the sparse prior underlying HSIs, a sparse HSI super-resolution model was proposed in [16].…”

Section: Introductionmentioning

confidence: 99%

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Hyperspectral Image Super-Resolution via Nonlocal Low-Rank Tensor Approximation and Total Variation Regularization

et al. 2017

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Hyperspectral image (HSI) possesses three intrinsic characteristics: the global correlation across spectral domain, the nonlocal self-similarity across spatial domain, and the local smooth structure across both spatial and spectral domains. This paper proposes a novel tensor based approach to handle the problem of HSI spatial super-resolution by modeling such three underlying characteristics. Specifically, a noncovex tensor penalty is used to exploit the former two intrinsic characteristics hidden in several 4D tensors formed by nonlocal similar patches within the 3D HSI. In addition, the local smoothness in both spatial and spectral modes of the HSI cube is characterized by a 3D total variation (TV) term. Then, we develop an effective algorithm for solving the resulting optimization by using the local linear approximation (LLA) strategy and the alternative direction method of multipliers (ADMM). A series of experiments are carried out to illustrate the superiority of the proposed approach over some state-of-the-art approaches.

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Section: Tv Regularizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Hyperspectral Image Super-Resolution via Nonlocal Low-Rank Tensor Approximation and Total Variation Regularization

et al. 2017

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“…Here each pixel is divided to a specified number of subpixels, wich are rearranged according to the endmembers and its fractional abundance using e.g. : spatial regularization tehniques (Villa et al, 2010), total variation minimization (Guo et al, 2009), or Hopfield neural network optimization (Nguyen et al, 2006). The main advantage of these methods is that they do not require any other information as contained in the hyperspectral image itself.…”

Section: Introductionmentioning

confidence: 99%

Hyperspectral Image Resolution Enhancement Based on Spectral Unmixing and Information Fusion

Bieniarz

Cerra

Avbelj

et al. 2012

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.

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ABSTRACT:Hyperspectral imaging sensors exibit high spectral resolution, but normally low spatial resolution. This leads to spectral signatures of pixels originating from different object types. Such pixels are called mixed pixels. Spectral unmixing methods can be employed to estimate the fractions of reflected light from the different objects within the pixel area. However, spectral unmixing does not provide any spatial information about the sources and therefore additional information is needed to precisely locate the sources. In order to restore the spatial information of hyperspectral images we propose a hyperspectral and multispectral image fusion method based on spectral unmixing. The algorithm is tested with HyMAP image data consisting of 125 spectral bands and a simulated multispectral image consisting of 8 bands.

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“…As a result, these methods suffer from numerical problems for smaller values of p. Thus, an attractive solution is to employ Lipschitz continuous approximations, such as the exponential function, the logarithm function or sigmoid functions, e.g., [20,23,34]. The arctan function is also used in different literature works for sparse regularization, such as approximating the sign function appearing in the derivative of the 1 -norm term in [35], introducing a penalty function for the sparse signal estimation by the maximally-sparse convex approach in [36] or approximating the 0 -norm term through a weighted 1 -norm term in [23].…”

Section: Introductionmentioning

confidence: 99%

ℓ0-Norm Sparse Hyperspectral Unmixing Using Arctan Smoothing

et al. 2016

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Abstract:The goal of sparse linear hyperspectral unmixing is to determine a scanty subset of spectral signatures of materials contained in each mixed pixel and to estimate their fractional abundances. This turns into an 0 -norm minimization, which is an NP-hard problem. In this paper, we propose a new iterative method, which starts as an 1 -norm optimization that is convex, has a unique solution, converges quickly and iteratively tends to be an 0 -norm problem. More specifically, we employ the arctan function with the parameter σ ≥ 0 in our optimization. This function is Lipschitz continuous and approximates 1 -norm and 0 -norm for small and large values of σ, respectively. We prove that the set of local optima of our problem is continuous versus σ. Thus, by a gradual increase of σ in each iteration, we may avoid being trapped in a suboptimal solution. We propose to use the alternating direction method of multipliers (ADMM) for our minimization problem iteratively while increasing σ exponentially. Our evaluations reveal the superiorities and shortcomings of the proposed method compared to several state-of-the-art methods. We consider such evaluations in different experiments over both synthetic and real hyperspectral data, and the results of our proposed methods reveal the sparsest estimated abundances compared to other competitive algorithms for the subimage of AVIRIS cuprite data.

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L1 unmixing and its application to hyperspectral image enhancement

Cited by 112 publications

References 16 publications

Hyperspectral Image Super-Resolution via Nonlocal Low-Rank Tensor Approximation and Total Variation Regularization

Hyperspectral Image Super-Resolution via Nonlocal Low-Rank Tensor Approximation and Total Variation Regularization

Hyperspectral Image Resolution Enhancement Based on Spectral Unmixing and Information Fusion

ℓ0-Norm Sparse Hyperspectral Unmixing Using Arctan Smoothing

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