Hyperspectral unmixing is a process of extracting hidden spectral signatures (or endmembers) and ... more Hyperspectral unmixing is a process of extracting hidden spectral signatures (or endmembers) and the corresponding proportions (or abundances) of a scene, from its hyperspectral observations. Motivated by Craig's belief, we recently proposed an alternating linear programming based hyperspectral unmixing algorithm called minimum volume enclosing simplex (MVES) algorithm, which can yield good unmixing performance even for instances of highly mixed data. In this paper, we propose a robust MVES algorithm called RMVES algorithm, which involves probabilistic reformulation of the MVES algorithm, so as to account for the presence of noise in the observations. The problem formulation for RMVES algorithm is manifested as a chance constrained program, which can be suitably implemented using sequential quadratic programming (SQP) solvers in an alternating fashion. Monte Carlo simulations are presented to demonstrate the efficacy of the proposed RMVES algorithm over several existing benchmark hyperspectral unmixing methods, including the original MVES algorithm.
In this paper, we describe a continuous optimization perspective on Winter's simplex volume maxim... more In this paper, we describe a continuous optimization perspective on Winter's simplex volume maximization belief for endmember ex traction in hyperspectral remote sensing. Winter's belief, proposed in the late 90's, is very insightful and has led to one of the most widely used class of endmember extraction algorithms nowadays- N-FINDR. Our endeavor to revisit this problem is to provide an al ternative, systematic, framework of formulating and understanding Winter's belief. Under the continuous optimization formulation of Winter's belief, we show a fundamental result that the existence of pure pixels is not only sufficient for the Winter problem to perfectly identify the ground-truth endmembers, but also necessary. Then, we derive two Winter-based algorithms based on two different optimization strategies. Interestingly, the resulting algorithms are found to be similar to an N-FINDR variant and the vertex component analysis (VCA) algorithm. Hence, the developed framework provides linkage and alternative interpretations to these existing algorithms. Simulation results are also presented to compare the derived Winter algorithms and several existing algorithms.
Endmember extraction is of prime importance in the process of hyperspectral unmixing so as to stu... more Endmember extraction is of prime importance in the process of hyperspectral unmixing so as to study the mineral composition of a landscape from its hyperspectral observations. Though, a whole bunch of pure-pixel based endmember extraction algorithms exists, the quest for a reliable, repeatable, and computationally efficient endmember extraction algorithm still prevails. In this work, we propose two pure-pixel based endmember extraction algorithms called simplex estimation by projection (SIMPLE-Pro) algorithm and p-norm based pure pixel identification (TRI-P) algorithm. The end member identifiability of the proposed two algorithms is theoretically proved under the pure pixel assumption. Both algorithms never require any initializations and hence they are repeatable. Monte Carlo simulations are performed to demonstrate the superior efficacy and computational efficiency of the proposed two algorithms over some existing benchmark endmember extraction algorithms.
IEEE Transactions on Geoscience and Remote Sensing, 2011
Effective unmixing of hyperspectral data cube under a noisy scenario has been a challenging resea... more Effective unmixing of hyperspectral data cube under a noisy scenario has been a challenging research problem in re- mote sensing arena. A branch of existing hyperspectral unmixing algorithms is based on Craig's criterion, which states that the ver- tices of the minimum-volume simplex enclosing the hyperspectral data should yield high fidelity estimates of the endmember signa- tures associated with the
Dynamic contrast enhanced magnetic resonance (DCE-MR) imaging is an exciting tool to study the ph... more Dynamic contrast enhanced magnetic resonance (DCE-MR) imaging is an exciting tool to study the pharmacokinetics of a suspected tumor tissue. Nonetheless, the inevitable partial volume effect in DCE-MR images may seriously hinder the quantitative analysis of the kinetic parameters. In this work, based on the conventional three-tissue compartment model, we propose an unsupervised nonnegative blind source separation (nBSS) algorithm, called
Accurate estimation of endmember signatures and the associated abundances of a scene from its hyp... more Accurate estimation of endmember signatures and the associated abundances of a scene from its hyperspectral observations is at present, a challenging research area. Many of the existing hyper-spectral unmixing algorithms are based on Winter's belief, which states that the vertices of the maximum volume simplex inside the data cloud (observations) will yield high fidelity estimates of the endmember signatures if pure-pixels exist. Based on Winter's belief, we recently proposed a convex analysis based alternating volume maximization (AVMAX) algorithm. In this paper we develop a robust version of the AVMAX algorithm. Here, the presence of noise in the hyperspectral observations is taken into consideration with the original deterministic constraints suitably reformulated as probabilistic constraints. The subproblems involved are convex problems and they can be effectively solved using available convex optimization solvers. Monte Carlo simulations are presented to demonstrate the efficacy of the proposed RAVMAX algorithm over several existing pure-pixel based hyperspectral unmixing methods, including its predecessor, the AVMAX algorithm.
IEEE Transactions on Geoscience and Remote Sensing, 2011
In the late 1990s, Winter proposed an endmember extraction belief that has much impact on endmemb... more In the late 1990s, Winter proposed an endmember extraction belief that has much impact on endmember extraction techniques in hyperspectral remote sensing. The idea is to find a maximum-volume simplex whose vertices are drawn from the pixel vectors. Winter's belief has stimulated much interest, resulting in many different variations of pixel search algorithms, widely known as N-FINDR, being proposed. In this paper, we take a continuous optimization perspective to revisit Winter's belief, where the aim is to provide an alternative framework of formulating and understanding Winter's belief in a systematic manner. We first prove that, fundamentally, the existence of pure pixels is not only sufficient for the Winter problem to perfectly identify the ground-truth endmembers but also necessary. Then, under the umbrella of the Winter problem, we derive two methods using two different optimization strategies. One is by alternating optimization. The resulting algorithm turns out to be an N-FINDR variant, but, with the proposed formulation, we can pin down some of its convergence characteristics. Another is by successive optimization; interestingly, the resulting algorithm is found to exhibit some similarity to vertex component analysis. Hence, the framework provides linkage and alternative interpretations to these existing algorithms. Furthermore, we propose a robust worst case generalization of the Winter problem for accounting for perturbed pixel effects in the noisy scenario. An algorithm combining alternating optimization and projected subgradients is devised to deal with the problem. We use both simulations and real data experiments to demonstrate the viability and merits of the proposed algorithms.
We recently reported an iterative non-negative blind source separation (nBSS) method, called conv... more We recently reported an iterative non-negative blind source separation (nBSS) method, called convex analysis of mixtures of nonnegative sources via alternating volume maximization (CAMNSAVM) [1], and demonstrated that it provides promising separation performance in image analysis. Nonetheless, the amount of data may be quite large in practical applications, and this may limit the real-time applicability of CAMNS-AVM. In this paper,
Hyperspectral unmixing is a process of extracting hidden spectral signatures (or endmembers) and ... more Hyperspectral unmixing is a process of extracting hidden spectral signatures (or endmembers) and the corresponding proportions (or abundances) of a scene, from its hyperspectral observations. Motivated by Craig's belief, we recently proposed an alternating linear programming based hyperspectral unmixing algorithm called minimum volume enclosing simplex (MVES) algorithm, which can yield good unmixing performance even for instances of highly mixed data. In this paper, we propose a robust MVES algorithm called RMVES algorithm, which involves probabilistic reformulation of the MVES algorithm, so as to account for the presence of noise in the observations. The problem formulation for RMVES algorithm is manifested as a chance constrained program, which can be suitably implemented using sequential quadratic programming (SQP) solvers in an alternating fashion. Monte Carlo simulations are presented to demonstrate the efficacy of the proposed RMVES algorithm over several existing benchmark hyperspectral unmixing methods, including the original MVES algorithm.
In this paper, we describe a continuous optimization perspective on Winter's simplex volume maxim... more In this paper, we describe a continuous optimization perspective on Winter's simplex volume maximization belief for endmember ex traction in hyperspectral remote sensing. Winter's belief, proposed in the late 90's, is very insightful and has led to one of the most widely used class of endmember extraction algorithms nowadays- N-FINDR. Our endeavor to revisit this problem is to provide an al ternative, systematic, framework of formulating and understanding Winter's belief. Under the continuous optimization formulation of Winter's belief, we show a fundamental result that the existence of pure pixels is not only sufficient for the Winter problem to perfectly identify the ground-truth endmembers, but also necessary. Then, we derive two Winter-based algorithms based on two different optimization strategies. Interestingly, the resulting algorithms are found to be similar to an N-FINDR variant and the vertex component analysis (VCA) algorithm. Hence, the developed framework provides linkage and alternative interpretations to these existing algorithms. Simulation results are also presented to compare the derived Winter algorithms and several existing algorithms.
Endmember extraction is of prime importance in the process of hyperspectral unmixing so as to stu... more Endmember extraction is of prime importance in the process of hyperspectral unmixing so as to study the mineral composition of a landscape from its hyperspectral observations. Though, a whole bunch of pure-pixel based endmember extraction algorithms exists, the quest for a reliable, repeatable, and computationally efficient endmember extraction algorithm still prevails. In this work, we propose two pure-pixel based endmember extraction algorithms called simplex estimation by projection (SIMPLE-Pro) algorithm and p-norm based pure pixel identification (TRI-P) algorithm. The end member identifiability of the proposed two algorithms is theoretically proved under the pure pixel assumption. Both algorithms never require any initializations and hence they are repeatable. Monte Carlo simulations are performed to demonstrate the superior efficacy and computational efficiency of the proposed two algorithms over some existing benchmark endmember extraction algorithms.
IEEE Transactions on Geoscience and Remote Sensing, 2011
Effective unmixing of hyperspectral data cube under a noisy scenario has been a challenging resea... more Effective unmixing of hyperspectral data cube under a noisy scenario has been a challenging research problem in re- mote sensing arena. A branch of existing hyperspectral unmixing algorithms is based on Craig's criterion, which states that the ver- tices of the minimum-volume simplex enclosing the hyperspectral data should yield high fidelity estimates of the endmember signa- tures associated with the
Dynamic contrast enhanced magnetic resonance (DCE-MR) imaging is an exciting tool to study the ph... more Dynamic contrast enhanced magnetic resonance (DCE-MR) imaging is an exciting tool to study the pharmacokinetics of a suspected tumor tissue. Nonetheless, the inevitable partial volume effect in DCE-MR images may seriously hinder the quantitative analysis of the kinetic parameters. In this work, based on the conventional three-tissue compartment model, we propose an unsupervised nonnegative blind source separation (nBSS) algorithm, called
Accurate estimation of endmember signatures and the associated abundances of a scene from its hyp... more Accurate estimation of endmember signatures and the associated abundances of a scene from its hyperspectral observations is at present, a challenging research area. Many of the existing hyper-spectral unmixing algorithms are based on Winter's belief, which states that the vertices of the maximum volume simplex inside the data cloud (observations) will yield high fidelity estimates of the endmember signatures if pure-pixels exist. Based on Winter's belief, we recently proposed a convex analysis based alternating volume maximization (AVMAX) algorithm. In this paper we develop a robust version of the AVMAX algorithm. Here, the presence of noise in the hyperspectral observations is taken into consideration with the original deterministic constraints suitably reformulated as probabilistic constraints. The subproblems involved are convex problems and they can be effectively solved using available convex optimization solvers. Monte Carlo simulations are presented to demonstrate the efficacy of the proposed RAVMAX algorithm over several existing pure-pixel based hyperspectral unmixing methods, including its predecessor, the AVMAX algorithm.
IEEE Transactions on Geoscience and Remote Sensing, 2011
In the late 1990s, Winter proposed an endmember extraction belief that has much impact on endmemb... more In the late 1990s, Winter proposed an endmember extraction belief that has much impact on endmember extraction techniques in hyperspectral remote sensing. The idea is to find a maximum-volume simplex whose vertices are drawn from the pixel vectors. Winter's belief has stimulated much interest, resulting in many different variations of pixel search algorithms, widely known as N-FINDR, being proposed. In this paper, we take a continuous optimization perspective to revisit Winter's belief, where the aim is to provide an alternative framework of formulating and understanding Winter's belief in a systematic manner. We first prove that, fundamentally, the existence of pure pixels is not only sufficient for the Winter problem to perfectly identify the ground-truth endmembers but also necessary. Then, under the umbrella of the Winter problem, we derive two methods using two different optimization strategies. One is by alternating optimization. The resulting algorithm turns out to be an N-FINDR variant, but, with the proposed formulation, we can pin down some of its convergence characteristics. Another is by successive optimization; interestingly, the resulting algorithm is found to exhibit some similarity to vertex component analysis. Hence, the framework provides linkage and alternative interpretations to these existing algorithms. Furthermore, we propose a robust worst case generalization of the Winter problem for accounting for perturbed pixel effects in the noisy scenario. An algorithm combining alternating optimization and projected subgradients is devised to deal with the problem. We use both simulations and real data experiments to demonstrate the viability and merits of the proposed algorithms.
We recently reported an iterative non-negative blind source separation (nBSS) method, called conv... more We recently reported an iterative non-negative blind source separation (nBSS) method, called convex analysis of mixtures of nonnegative sources via alternating volume maximization (CAMNSAVM) [1], and demonstrated that it provides promising separation performance in image analysis. Nonetheless, the amount of data may be quite large in practical applications, and this may limit the real-time applicability of CAMNS-AVM. In this paper,
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