Multiobjective Optimized Endmember Extraction for Hyperspectral Image

Abstract

Endmember extraction (EE) is one of the most important issues in hyperspectral mixture analysis. It is also a challenging task due to the intrinsic complexity of remote sensing images and the lack of priori knowledge. In recent years, a number of EE methods have been developed, where several different optimization objectives have been proposed from different perspectives. In all of these methods, only one objective function has to be optimized, which represents a specific characteristic of endmembers. However, one single-objective function may not be able to express all the characteristics of endmembers from various aspects, which would not be powerful enough to provide satisfactory unmixing results because of the complexity of remote sensing images. In this paper, a multiobjective discrete particle swarm optimization algorithm (MODPSO) is utilized to tackle the problem of EE, where two objective functions, namely, volume maximization (VM) and root-mean-square error (RMSE) minimization are simultaneously optimized. Experimental results on two real hyperspectral images show the superiority of the proposed MODPSO with respect to the single objective D-PSO method, and MODPSO still needs further improvement on the optimization of the VM with respect to other approaches.

Two-Stage Evolutionary Algorithm Based on Subspace Specified Searching for Hyperspectral Endmember Extraction

“…Y and Y ˆ represent the original image and the reconstructed image, respectively. The abundance for reconstructing the image is calculated by the unconstrained least squares (UCLS) [52] using the following formulas: (6) where A is the endmember matrix, and S ˆ is the estimated abundance matrix.…”

“…To better suit real-world application, multi-objective EE was put forward to simultaneously optimize the two conflict objective functions, thus providing adjustable options to users. The multi-objective discrete particle swarm optimization algorithm (MODPSO) [52] was originally proposed to produce trade-off solutions between the reconstructed error and volume objective functions. Later on, several improved algorithms [53][54][55][56] were developed with the purpose of reaching a better Pareto front.…”

An Adaptive Surrogate-Assisted Endmember Extraction Framework Based on Intelligent Optimization Algorithms for Hyperspectral Remote Sensing Images

“…In addition, refs. [18,22,[25][26][27]29] have turned to multiobjective optimization algorithms to optimize two indicators simultaneously, namely minimizing the RMSE and maximizing the volume.…”

“…In order to alleviate the above problems, some intelligent optimization algorithms have been applied in endmember extraction in recent years. In the literature, the intelligent-based endmember extraction algorithms can be roughly divided into three main categories, which are the based on the genetic algorithms (GA) [17][18][19][20], the particle swarm optimization (PSO) algorithms [21][22][23][24][25][26][27] and the differential evolution (DE) algorithms [28,29]. Zhang et al [21] employed the discrete particle swarm optimization (DPSO) to minimize the root mean square error (RMSE) between the reconstructed image and the original image to obtain the appropriate endmember set by encoding each particle as the potential position of the active endmember in the hyperspectral image.…”

Endmember Bundle Extraction Based on Multiobjective Optimization

“…Another objective function used in the intelligent optimization-based methods is the maximization of the volume of the simplex constructed by the chosen endmembers. It has been shown that the EE results obtained by these two objective functions are different [38]. In order to get robust results for different real images, multiobjective optimization is used to simultaneously optimize the two objective functions [39], [40].…”