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7738 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 52, NO. 12, DECEMBER 2014

Spectral–Spatial Hyperspectral Image Classiﬁcation

via Multiscale Adaptive Sparse Representation

Leyuan Fang, Member, IEEE, Shutao Li, Member, IEEE, Xudong Kang, Student Member, IEEE,and

Jón Atli Benediktsson, Fellow, IEEE

Abstract—Sparse representation has been demonstrated to be

a powerful tool in classiﬁcation of hyperspectral images (HSIs).

The spatial context of an HSI can be exploited by ﬁrst deﬁning

a local region for each test pixel and then jointly representing

pixels within each region by a set of common training atoms

(samples). However, the selection of the optimal region scale (size)

for different HSIs with different types of structures is a nontrivial

task. In this paper, considering that regions of different scales

incorporate the complementary yet correlated information for

classiﬁcation, a multiscale adaptive sparse representation (MASR)

model is proposed. The MASR effectively exploits spatial infor-

mation at multiple scales via an adaptive sparse strategy. The

adaptive sparse strategy not only restricts pixels from different

scales to be represented by training atoms from a particular class

but also allows the selected atoms for these pixels to be varied, thus

providing an improved representation. Experiments on several

real HSI data sets demonstrate the qualitative and quantitative

superiority of the proposed MASR algorithm when compared to

several well-known classiﬁers.

Index Terms—Classiﬁcation, hyperspectral image (HSI), mul-

tiscale adaptive sparse representation (MASR), multiscale spatial

information, sparse representation.

I. INTRODUCTION

OR many years, classiﬁcation of remote sensing images

has played an essential role in several applications, includ-

ing assessment of environmental damage, growth regulation,

land-use monitoring, urban planning, and reconnaissance [1].

Compared with high spatial resolution images (e.g., single-band

panchromatic data), hyperspectral images (HSIs) have a much

higher spectral resolution and thus give the possibility to detect

and distinguish various objects with higher accuracy [2].

In HSIs, each pixel is a high-dimensional vector, whose

entries denote the spectral response from hundreds of spectral

bands, spanning from the visible to the infrared spectrum [3].

The objective of HSI classiﬁcation is to categorize each spectral

Manuscript received October 11, 2013; revised January 12, 2014 and

March 21, 2014; accepted April 12, 2014. Date of publication May 6, 2014;

date of current version June 12, 2014. This work was supported in part by

the National Natural Science Foundation of China under Grant 61172161; by

the National Natural Science Foundation for Distinguished Young Scholars of

China under Grant 61325007; by the Fundamental Research Funds for the

Central Universities, Hunan University; and by the Scholarship Award for

Excellent Doctoral Student granted by the Chinese Ministry of Education.

L. Fang, S. Li, and X. Kang are with the College of Electrical and

Information Engineering, Hunan University, Changsha 410082, China (e-mail:

fangleyuan@gmail.com; shutao_li@hnu.edu.cn; xudong kang@163.com).

J. A. Benediktsson is with the Faculty of Electrical and Computer Engineer-

ing, University of Iceland, 101 Reykjavk, Iceland (e-mail: benedikt@hi.is).

Color versions of one or more of the ﬁgures in this paper are available online

at http://ieeexplore.ieee.org.

Digital Object Identiﬁer 10.1109/TGRS.2014.2318058

pixel belonging to one of the classes based on the spectral

information. To achieve this objective, many spectral pixelwise

classiﬁers have been developed, including the support vector

machine (SVM) [4]–[6], support vector conditional random

classiﬁer [7], multinomial logistic regression [8], [9], neural

network [10], adaptive artiﬁcial immune network [11], and

artiﬁcial deoxyribonucleic acid computing [12]. In general,

although these classiﬁers can make a full use of the spectral

information of HSI, the spatial context is not considered by

them. Therefore, the obtained classiﬁcation maps often appear

noisy. Recently, to enhance the classiﬁcation performance,

many attempts have been made to incorporate the spatial in-

formation of HSI, based on the assumption that pixels within

a local region usually represent the same material and have

similar spectral characteristics [13]. In [14], the spatial coher-

ence of pixels within a local region is utilized by including a

postprocessing procedure for each individual label. In [15] and

[16], the spectral and spatial information of each HSI pixel

is combined via a composite kernel approach. In [17], the

statistical dependence among neighboring pixels is exploited

by a Bayesian-based approach. In addition, some other HSI

classiﬁcation works have focused on effective feature extraction

or feature reduction approaches, including spectral-only based

(e.g., principal components analysis [18], linear discriminative

analysis [19], and clonal selection for feature selection [20])

and spectral–spatial based (e.g., local Fisher’s discriminant [21]

and extended morphological proﬁles (EMPs) [22]). Moreover,

multiple features extracted from different ways can be com-

bined to further increase the robustness of classiﬁcation [23].

Motived by the sparse coding mechanism of human vision

systems [24], sparse representation [25] has been demonstrated

to be an extremely powerful tool in many signal processing

applications, such as denoising [26], [27], interpolation [28],

and fusion [29]. Recently, the sparse representation has also

been extended to HSI classiﬁcation [30]–[33] based on the

observation that HSI pixels belonging to the same class often

lie in a low-dimensional subspace, which is spanned by the

dictionary atoms (training samples) of the same class. Thus, an

unknown test pixel to be classiﬁed can be sparsely represented

by a few atoms among the whole training dictionary. The class

label of the test pixel can be determined by the recovered sparse

coefﬁcients, which contain the positions of the selected atoms

and their weight values. Moreover, to further exploit the spatial

context of HSI, a joint sparse representation model (JSRM) can

be employed [30], [34]. The JSRM ﬁrst deﬁnes a local region of

ﬁxed size for each test pixel and then simultaneously represents

pixels within each local region by a set of common atoms.

IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.

See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

FANG et al.: SPECTRAL–SPATIAL HSI CLASSIFICATION VIA MASR 7739

Compared to the spectral-only pixelwise sparse representation

approach, the JSRM can achieve a better HSI classiﬁcation per-

formance, in terms of accuracy. However, regions with different

spatial structures in HSI should beneﬁt from varied region sizes.

For example, a small region size is appropriate for detailed

or near-edge regions, while smooth areas require large region

sizes. Therefore, the JSRM is sensitive to the size of regions,

and it is very difﬁcult to determine the optimal region size for

the method.

For one speciﬁc test pixel, when its neighboring region

scales (sizes) are selected differently, distinct structures and

characteristics will be exhibited. Considering that neighboring

regions of different scales correspond to the same test pixel,

they should offer complementary yet correlated information for

classiﬁcation. Inspired by that, instead of selecting only a single

region scale, an effective multiscale scheme called the multi-

scale adaptive sparse representation (MASR) is proposed in this

paper to take advantage of correlations among multiple region

scales for HSI classiﬁcation. Motivated by works in [35] and

[36], the MASR simultaneously represents the pixels of multi-

ple scales via an adaptive sparse strategy. More speciﬁcally, as

pixels of different scales should belong to the same class, the

adaptive sparse strategy ﬁrst enforces pixels of multiple scales

to be represented by atoms from the same class. In addition,

since differences exist among varied scales, the adaptive sparse

strategy allows pixels of different scales to adaptively choose

their own appropriate atoms within each class. In this way, the

MASR not only combines the information of different scales

for discrimination but also achieves an effective representation

for each scale. We should note that the multiscale scheme has

been utilized in a sparse representation technique for restoration

problems and a more accurately reconstructed image has been

obtained [37], [38]. In addition, the multiscale information has

also been used for some recognition tasks [39], [40]. Different

from the proposed MASR algorithm, the multiscale information

was exploited by simply concatenating images of different

scales into a long vector in [39], or adaptively fusing the result

of each scale by a complex optimization method in [40].

The remainder of this paper is organized as follows: In

Section II, the pixelwise sparse representation and single-scale

JSRM techniques for HSI classiﬁcation are brieﬂy reviewed.

Section III introduces the proposed multiscale MASR model for

spectral–spatial HSI classiﬁcation. In Section IV, experimental

results on three test images are presented. Concluding remarks

and future research directions are given in Section V.

II. S

PAR SE REPRESENTATION FOR HSI CLASSIFICATION

A. Pixelwise Sparse Representation

The sparse representation classiﬁcation (SRC) framework

was ﬁrst introduced for face recognition [41]. Chen et al.

extended the SRC to pixelwise HSI classiﬁcation, which relied

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. An unknown test

pixel can be represented as a linear combination of training

pixels from all classes. Concretely, let y ∈ R

M×1

be a pixel

with M denoting the number of spectral bands and D =

,...,D

] ∈ R

M×N

be a structural dictionary,

where D

∈ R

M×N

, c =1,...,C is the cth class subdic-

tionary whose columns (atoms) are extracted from the training

pixels; C is the number of classes; N

is the number of atoms

in subdictionary D

; and N =



c=1

is the total number of

atoms in D. The test pixel y can be sparsely expressed as

y = Dα (1)

where α ∈ R

N×1

is a sparse coefﬁcient vector. Given the struc-

tural dictionaryD, the sparse coefﬁcient α can be recovered by

solving

α =argmin

y − Dα

subject to α

≤ K (2)

where K is a predeﬁned upper bound on the sparsity level,

representing the maximum number of selected atoms in the

dictionary (also corresponding to the nonzero coefﬁcients in

α).

In general, (2) is a nondeterministic polynomial-time hard (NP-

hard) [42] problem. However, it can be solved approximately by

the orthogonal matching pursuit (OMP) [43], [44]. To be more

speciﬁc, for a test pixel y, the OMP algorithm tends to ﬁnd a

representative atom at each iteration based on the correlation

between the dictionary D and the residual vector R, where

R = y − Dα. Basically, the OMP algorithm incoporates the

following steps at each iteration:

1) Compute the following residue correlation vector E ∈

N×1

E = D

R. (3)

2) Select a new representative atom (index i) based on the

current residual correlation vector

i =maxE

, i =1,...,N. (4)

3) Merge the newly selected atom’s index

i with the previ-

ously selected atom’s index set I, i.e.,

I = I ∪

i. (5)

4) Estimate sparse coefﬁcient α by projecting the test sub-

ject y on D

, i.e.,

α =





−1

y (6)

where the subdictionary D

is constructed using the

selected atoms.

Once the sparse coefﬁcient vector

α is obtained, the class

label of the test pixel y can be determined by the minimal

representation error between y and its approximation from the

subdictionary of each class, i.e.,

ˆc =argmin

y − D



,c=1,...,C (7)

where

contains the coefﬁcients in

α belonging to the cth

class.

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