Journal of Electrical and Computer Engineering

Volume 2017 (2017), Article ID 2683248, 17 pages

https://doi.org/10.1155/2017/2683248

## Subpixel Mapping Method of Hyperspectral Images Based on Modified Binary Quantum Particle Swarm Optimization

^{1}College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China^{2}Institute of Computer Application Technology, Hangzhou Dianzi University, Hangzhou 310018, China

Correspondence should be addressed to Xiaorun Li

Received 16 March 2017; Revised 31 May 2017; Accepted 3 July 2017; Published 6 August 2017

Academic Editor: Qunming Wang

Copyright © 2017 Shuhan Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Subpixel mapping technology can determine the specific location of different objects in the mixed pixel and effectively solve the uncertainty of the ground features spatial distribution in traditional classification technology. Existing methods based on linear optimization encounter the premature and local convergence of the optimization algorithm. This paper proposes a subpixel mapping method based on modified binary quantum particle swarm optimization (MBQPSO) to solve the above issues. The initial subpixel mapping imagery is obtained according to spectral unmixing results. We focus mainly on the discretization of QPSO, which is implemented by modifying the discrete update process of particle location, to minimize the objective function, which is formulated based on different connected regional perimeter calculating methods. To reduce time complexity, a target optimization strategy of global iteration combined with local iteration is performed. The MBQPSO is tested on standard test functions and results show that MBQPSO has the best performance on global optimization and convergent rate. Then, we analyze the proposed algorithm qualitatively and quantitatively by simulated and real experiment; results show that the method combined with MBQPSO and objective function, which is formulated based on the gap length between region and background, has the best performance in accuracy and efficiency.

#### 1. Introduction

Hyperspectral images are composed of hundreds of bands with a very high spectral resolution, generally from the visible to the infrared region. For every recorded pixel, rich spectral information provides a complete spectral description and a better characterization of the observed surface, which results in a very powerful tool for materials discrimination and earth observation. However, a common drawback of hyperspectral sensors is the relatively low spatial resolution, which leads to the problem of mixed pixels (e.g., pixels containing mixture of different materials). Ground feature spatial detail in mixed pixels is extremely important for land cover mapping, coast-line extraction, change detection, and landscape index estimating. Mixed pixels cannot be correctly addressed by traditional hard classification methods. Subpixel mapping is an effective measure to solve this problem.

Subpixel mapping and pixels spatial dependence theory were initially proposed by Atkinson [1]. Based on this theory, several subpixel mapping techniques have been proposed. Existing subpixel mapping methods contain the following typical algorithms: the neural network method, the geostatistics method, the Markov random field method, and the linear optimization method.

The first category is the neural network method. Among them, Hopfield’s neural network (HNN) model combined with the constrained energy minimization principle of output neuron has been used in the subpixel mapping. In the HNN model, each pixel is a neuron that constructs an energy function with the correlation between subpixels and the neighboring subpixel, using the mixed pixels abundance as the constraint [2, 3]. The improved HNN method for small scale targets and small scale coexisting with large scale target had been proposed in [4]. A Back Propagation (BP) neural network is trained to learn the appropriate location of the subpixels, which belongs to the different classes inside the pixel [5]. At the same time, wavelet transform and genetic algorithms have been used to solve subpixel mapping [6, 7]. The ARTMAP neural network [8] has been utilized to realize the learning model in [6]. Based on the subpixel shifted remote sensing images (SSRSI), component information obtained from SSRSI was put into the HNN model to increase ratio constraints and reduce uncertainty [9]. In order to eliminate isolated pixels, the results of the BP neural network model were postprocessed [10]. Multiple low spatial resolution subpixel shifted images were used to modify the BP neural network to reduce uncertainty and error in the BPNN model [11]. The general regression neural network (GRNN) has been proposed to achieve improved accuracy in subpixel mapping [12].

The second category is the geostatistics method. Existing approaches for subpixel mapping have been placed within an inverse problem framework; a geostatistical method was proposed for generating alternative synthetic land cover maps at the fine (target) spatial resolution [13, 14]. In [15], a model sequentially produced with local indicator variogram (SLIV) was proposed, and indicator variograms extracted from target-resolution classification were produced from a representative local area to develop an effective method.

The third category is the Markov random field method. The Markov random field (MRF) has been used in subpixel mapping [16]. Subsequently, scholars have done in-depth study on the MRF model [17, 18]. Considering the idea of the MRF, which is able to consider spatial and spectral information simultaneously, a novel sFCM-based (supervised fuzzy -means) subpixel mapping model that incorporates the sFCM criterion for unmixing pixels into the objective function was proposed [19]. In terms of the energy minimization for MRF, one of the most commonly used traditional methods is simulated annealing (SA), but SA is very time-consuming. To overcome this limitation, graph cut is used in [20].

The fourth category is the linear optimization method. Through the decomposition of mixed pixels or fuzzy classification technique, the proportion of features was determined and then a mathematical model was defined for describing the spatial correlation to construct the objective function, converting the subpixel mapping into a linear optimization problem. Among linear optimization method, Verhoeye proposed the maximum spatial correlation between neighborhood pixels and solved the problem using simplex linear optimization technology [21]. Immune clonal selection algorithms and differential evolution algorithms were used to solve the mathematical model using Verhoeye’s data [22, 23]. A new subpixel mapping method based on evolution agent was proposed [24]. Since subpixel/pixel spatial attraction model (SPSAM), which assumes that similar features have physical characteristics of mutual attraction, has effectively verified spatial correlation theory [25, 26], SPSAM ignores the correlation between subpixels. Wang put forward a modified SPSAM, which considers the correlation between and within the pixel simultaneously [27, 28]. By incorporating auxiliary datasets, a subpixel mapping framework based on a maximum a posteriori (MAP) model was proposed to utilize the complementary information of multiple shifted images [29]. Since the previous MAP-based subpixel mapping algorithm was obtained by downsampling a classification image without spectral unmixing errors, an adaptive subpixel mapping method based on a MAP model and a winner-take-all class determination strategy (AMCDSM) was proposed [30]. The existing spectral-spatial based SPM algorithms only use the maximal spatial dependence principle as the spatial term to describe the local spatial distribution of different land cover features; a novel spectral-spatial based SPM algorithm with multiscale spatial dependence was proposed [31]. In [32], the spectral unmixing predictions (i.e., coarse land cover proportions used as input for SPM) were considered a convolution of not only subpixels within the coarse pixel, but also subpixels from neighboring coarse pixels. A new SPM method based on optimization is developed which recognizes the optimal solution as the one that, when convolved with the PSF, is the same as the input coarse land cover proportion.

The computation complexity of those above objective functions is relatively highly complex. In order to intuitively reflect the spatial correlation, based on the principle that similar features attract each other, Villa utilized various types of regional perimeter minimum as a target after subpixel mapping, using the simulated annealing (SA) and pixel swapping algorithm (PSA) to achieve iterative optimization [33, 34]. Compared with SA and other similar evolutionary techniques, PSO has some attractive characteristics and has proven to have superior computational efficiency. This is because PSO is not applicable to problems where the position of the particle should be discrete [35]. Ertürk used binary particle swarm optimization (BPSO) to optimize the objective function that had been proposed by Villa, and the optimization algorithm has been fit for parallel implementation [35]. The results of the BPSO algorithm are better than SA. Compared with BPSO algorithm, Sun proposed the binary quantum particle swarm optimization algorithm (QPSO) [36], which demonstrates many advantages such as a simple evolution equation, fewer control parameters, fast convergence rate, and simple operation. Therefore, BQPSO algorithm was proposed for subpixel mapping [37], but the discrete update process of particle location may lead to algorithm premature convergence and local convergence. The modified version of BQPSO was proposed in this article.

In this study, a subpixel mapping method of hyperspectral images based on MBQPSO is proposed. The initial subpixel mapping imagery is obtained according to the results of spectral unmixing. Using regional perimeter minimizing to depict spatial correlation is intuitive and requires low computational complexity. The objective function is formulated by different connected regional perimeter calculating methods, such as the gap length between region and background (_gap), the length of chain code (_chain), and the sum of border point number (_point). We focus mainly on the discretization of QPSO, which is implemented by modifying the discrete update process of particle location, to minimize the above three objective functions. In order to reduce time complexity, objective optimization strategy of global iteration combined with local iteration is performed.

The rest of this paper is organized as follows. Section 2 presents the basic methodology of the proposed subpixel mapping method based on MBQPSO. Section 3 provides the experimental results and analyses with simulated and real hyperspectral images. The conclusion is drawn in Section 4.

#### 2. Subpixel Mapping Method Based on MBQPSO

The proposed method provides an accurate subpixel mapping method based on MBQPSO and local optimization strategy. In this paper, known endmembers and abundance are the premise of the subpixel mapping method. Specifically, the number of endmembers is estimated by VD [38] and extracted by VCA. Then, the abundance is obtained by FCLS in each pixel for each endmember. A pixel can be seen as a pure pixel only if the minimum difference value between the maximum abundance and the others in the pixel is greater than a certain threshold [33–35]. The initial subpixel mapping imagery is obtained according to spectral unmixing results.

Then the follow-up process of the proposed subpixel mapping algorithm based on MBQPSO consists of the following: () the objective function is formulated by different connected regional perimeter calculating methods; () the proposed MBQPSO is used to minimize the objective function; () optimization strategy of global iteration combined with local iteration is performed to reduce time complexity. The framework of the proposed subpixel mapping method is organized as follows: The objective function and adaptability analysis are presented in Section 2.1. The MBQPSO algorithm is introduced in Section 2.2. Two key problems of objective function optimization based on MBQPSO are described in Section 2.3 followed by the optimization strategy in Section 2.4.

##### 2.1. Modified Binary Quantum Particle Swarm Optimization Algorithm

Before presenting the proposed MBQPSO, we first introduce QPSO method, containing the basic concept and evolution equation. The discrete update process of evolution equation is given in the form of pseudocode, and the specific details of the discrete update process of are given in the form of textual description.

###### 2.1.1. QPSO Method

The QPSO algorithm [36] is theoretical a global convergence guaranteed algorithm, which has fewer parameters and better global searching ability than PSO. In QPSO algorithm, there are only the concepts of particle position and the distance between particles, while PSO includes the concept of speed and trajectory. In a QPSO, each particle only has position information in a -dimensional searching space. is the current time and is the th particle in particles. While time is , the optimal position of the th particle is and the global optimal position of particle swarm is . The evolution equations are as follows:where is a positive integer between 1 and ; and are random positive numbers between 0 and 1. If , then the plus/minus sign in (3) takes a plus sign, or else it takes a minus [36]. is the th particle attractor, represented by a random vector that is defined by (2). is the average optimal position; is contraction-expansion coefficient and determines the particle convergence speed. The expression is as follows: where curiteration is the current iteration number and maxiteration is the maximum iteration number. and are the initial and final value of the control parameter, respectively. In addition, is greater than, and is a linear decreasing function, controlled by the parameters.

However, like PSO and other evolutionary algorithms, QPSO readily relapses into local optimum when solving high-dimensional complex optimization problems. In order to adapt the QPSO algorithm to the practical problems in discrete search space, we introduce the concept of binary encoding to QPSO, which is implemented by modifying the discrete update process of particle location.

###### 2.1.2. MBQPSO Method

In BQPSO [37], particle position is represented as a binary string, and continuous evolution equations (1)–(3) are all discretized. The discrete update process of and is given in Algorithms 1 and 2.