IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 11, NO. 12, DECEMBER 2014 2055
Superresolution Mapping Using Multiple
Dictionaries by Sparse Representation
Huijuan Huang, Jing Yu, and Weidong Sun
Abstract—Superresolution mapping can predict the spatial lo-
cation of land cover classes within mixed pixels based on the spa-
tial dependence assumption. We propose a novel superresolution
mapping method via multidictionary-based sparse representation,
which is robust to noise in both the learning and class-allocation
process. In the proposed method, the subpixel number belonging
to each class is obtained according to the degree of spectral
distortion, and the distribution modes of different classes are
treated discriminatorily. The subpixel classification is performed
according to the normalized reconstruction errors by the learned
multiple distribution dictionaries. The experimental results show
that the proposed method has improved accuracy and robustness
for real imagery.
Index Terms—Multidictionary learning, sparse representation,
spatial dependence, superresolution mapping (SRM).
I. INTRODUCTION
I
N multispectral and hyperspectral images (MHSIs), each
pixel contains a spectral signature over many narrow con-
tinuous spectral bands, which makes the classification of land
cover possible based on their electromagnetic spectrum, not
just the visible spectrum. However, MHSIs are commonly
dominated by mixed pixels that contain more than one distinct
substance due to the intrinsic issues (e.g., imperfect imaging
optics and secondary illumination), as well as extrinsic issues
(e.g., atmospheric turbulence and diverse distributed land cover
classes).
Atkinson [1] first introduced the concept of superresolution
mapping (SRM) based on the assumption of spatial depen-
dence, which refers to the tendency that spatially proximate
observation of a given property to be more alike than more
distant observations. This technique uses the abundance yielded
by spectral unmixing as inputs, and its output is a high-spatial-
resolution (HR) land cover map. By SRM, original low-spatial-
resolution (LR) pixels are divided into several subpixels, and
the ultimate task is to assign each subpixel to a proper class. It
is also termed as subpixel mapping [2], [3]. The current SRM
methods can be roughly categorized into two groups [4]: spatial
Manuscript received November 5, 2013; revised February 25, 2014; accepted
April 8, 2014. This work was supported in part by the National Natural Science
Foundation under Grant 61171117, by the National Science and Technology
Pillar Program under Grant 2012BAH31B01, and by the Key Project of the
Science and Technology Development Program of BEC of China under Grant
kz201310028035.
The authors are with the Department of Electronic Engineering, Tsinghua
University, Beijing 100084, China (e-mail: hhj09@mails.tsinghua.edu.cn;
yujing@tsinghua.edu.cn; wdsun@tsinghua.edu.cn).
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/LGRS.2014.2318758
optimization types [2], [3], [5], [6] and learning-based types
[7]–[10]. The first group involves optimizing a spatial regu-
larization model that reflects the spatial dependence, whereas
the second group learns prior information of distribution modes
from known data through neural networks or other learning
methods. In this letter, we focus on the latter category.
The overfitting problem is common in most of the neural-
network-learning-based SRM methods, which are also sensitive
to noise both in the learning and class-allocation process. In
addition, most of the current SRM methods strictly or to a large
extent maintain the number of subpixels belonging to each class
only according to the abundance. More importantly, current
methods usually treat all classes equally and learn only one
distribution mode, which may not be reasonable. For example,
rivers usually distribute linearly, whereas islands distribute as
oval areas, and they should be treated differently.
In natural images, the widely existed many similar patches
can be learned to formulate dictionaries via sparse represen-
tation to do image processing task [11], [12]. Similarly, in
land cover maps, there also exist repetitive spatial structures,
such as linearly distributed rivers. Based on this assumption,
we propose a novel SRM method via multidictionary-based
sparse representation. In this letter, we propose a feature vector
that captures the significant information about spatial depen-
dence and learns the distribution dictionary for each class
via sparse representation. In the class-allocation process, the
feature vector of the underlying subpixel is reconstructed by
every dictionary and is assigned to a class according to the
reconstruction errors and introduced spectrum distortions. Our
framework treats every land cover class discriminatorily, lead-
ing to more accurate distribution dictionaries. It is worth noting
that the sparse representation learning skill is robust to noise,
which has been demonstrated in the face recognition method
[12]. Moreover, the sparse representation has been successfully
applied in classification at pixel scale [13].
The rest of this letter is organized as follows. Section II
presents the proposed method, referred to as MSRSM. The
results of experiments are discussed in Section III. Finally, the
conclusion is drawn in Section IV.
II. P
ROPOSED METHOD
The proposed method can be divided into two steps: learning
and SRM. In the learning step, the training sample sets are first
extracted from the HR training land cover maps, which can
encode the spatial dependence effectively. Then, the multiple
distribution dictionaries are learned via sparse representation.
In the SRM step, the feature vector of the underlying subpixel is
1545-598X © 2014
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.
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