**1. Introduction**

Hyperspectral images have been widely applied to remote sensing image applications, such as land cover classification [1], target detection [2], anomaly detection [3], spectral unmixing [4] and others. Each pixel in HSI has hundreds of narrow contiguous bands, spanning from visible to infrared spectrum [5], which makes it possible to detect and distinguish various objects with higher accuracy [6]. However, increasing the number of spectral bands or features of an HSI pixel does not always help to increase the classification accuracy. Therefore, how to make full use of the information in HSIs is a problem in practical applications.

Many algorithms have been developed for the classification of HSIs. Among these, there are some well-known pixelwise classifiers, such as the support vector machine (SVM) [7–9], support vector conditional random classifier [10], multinomial logistic regression [11], neural network [12] and adaptive artificial immune network [13]. These pixelwise classifiers can make full use of the spectral information of HSIs, but the classification results are often noisy because the spatial information is not considered.

Therefore, some recent researches incorporated the spatial information in HSI classification to enhance the classification performance. The basic way to use spatial information is to assume that the pixels within a local region usually represent the same material and have similar spectral

characteristics [1]. Various researches [14–25] have been done based on this assumption. Besides these researches, Sparse representation (SR), which is based on the observation that spectral pixels of a particular class should lie in a low-dimensional subspace spanned by dictionary atoms (training pixels) from the same class, is also employed. In [26], a Joint Sparse Representation Classification (JSRC) method has been proposed to incorporate spectral information and spatial information. The spatial information is expressed by a fixed-size local square window centered with the test pixel. Then all pixels in the window are simultaneously joint represented by a few common atoms in the specified dictionary. The JSRC can achieve a good performance but the optimal size of the window cannot be determined easily. In [27], a stepwise Markov random field (MRF) optimization was proposed to exploit spatial information based on the result of multitask joint sparse representation. In [28], MASR was proposed to release the difficulty in choosing region size. Instead of choosing a single scale, this method extends the spatial information to several scales to take advantage of correlations among multiple region scales for HSI classification. But the multiscale regions used in MASR refer to multiscale patches which may contain noise pixels. Better than patch region, shape-adaptive superpixel can provide more accurate spatial information. In [29], the superpixel was introduced to replace the patch region. Then a shape-adaptive local smooth region was generated for each test pixel by a shape-adaptive algorithm in [30]. The latest research proposed a Multiscale Superpixel-Based Sparse Representation [31]. In this research, multiscale superpixels were generated and then each scale was represented by JSRC. Finally, a fusion result was gotten from multiscale results by majority voting. But the selection of scales for superpixels is still a problem. Although it uses multiscale to release the difficulty of selecting segmentation scale, it still needs a fundamental number of superpixels determined empirically.

In fact, patch and superpixel both have their own advantages and shortages. The patch can include all nearest neighbors but it also may contain noise pixels. Shape-adaptive superpixel can exploit more accurate spatial information but there are still some mixed superpixels when the scale is not optimal. In a mixed superpixel, there must be wrong representation because all pixels in the superpixel share the same representation. Inspired by merits and demerits of patch and superpixel, we propose to use a union region to replace the patch and superpixel. Union region refers to the overlap of patch and superpixel. Compared with patch, union region includes more similar pixels for the test pixel aiming at decreasing the effect of noise pixels. Compared with superpixel, union region provides more direct neighbors for the test pixel to enhance the representation of pixels located in the wrong superpixel. In addition, the required superpixels for generating union regions don't need empirical scale. The scales are determined by the size of the image and the corresponding patch sizes. By replacing patch in MASR with union region, we ge<sup>t</sup> a new algorithm called Multiscale Union Regions Adaptive Sparse Representation (MURASR). MURASR also adopts a probability majority voting method to optimize the classification result generated from the sparse representation. Experiment results show that the union region based algorithms always perform better than patch region based algorithms and the proposed MURASR outperforms other algorithms in terms of quantitative metrics and visual quality on the classification maps.

The rest parts of the paper are organized as follows. The JSRC and MASR are briefly introduced in Section 2. The details of proposed MURASR method are described in Section 3. The experimental results and discussions are presented in Section 4. Finally, Section 5 summarizes the paper and future works are suggested. The outline of the MURASR is illustrated in Figure 1.

**Figure 1.** Outline of the proposed MURASR framework.
