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An Online Coupled Dictionary Learning Approach

for Remote Sensing Image Fusion

Min Guo, Hongyan Zhang, Member, IEEE, Jiayi Li, Student Member, IEEE,

Liangpei Zhang, Senior Member, IEEE, and Huanfeng Shen, Senior Member, IEEE

Abstract—Most earth observation satellites, such as IKONOS,

QuickBird, GeoEye, and WorldView-2, provide a high spatial

resolution (HR) panchromatic (Pan) image and a multispectral

(MS) image at a lower spatial resolution (LR). Image fusion is an

effective way to acquire the HR MS images that are widely used in

various applications. In this paper, we propose an online coupled

dictionary learning (OCDL) approach for image fusion, in which a

superposition strategy is applied to construct the coupled dictio-

naries. The constructed coupled dictionaries are further developed

via an iterative update to ensure that the HR MS image patch can be

almost identically reconstructed by multiplying the HR dictionary

and the sparse coefﬁcient vector, which is solved by sparsely

representing its counterpart LR MS image patch over the LR

dictionary. The fusion results from IKONOS and WorldView-2

data show that the proposed fusion method is competitive or even

superior to the other state-of-the-art fusion methods.

Index Terms—Coupled dictionary, image fusion, remote sensing

imagery, sparse representation (SR).

I. INTRODUCTION

S A POWERFUL quality improvement technique, data

fusion has been gradually improved in recent years. In [1],

data fusion is deﬁned as a formal framewo rk which includes

expressed means and tools for combining and utilizing data

originating from different sources. Accounting for most of the

data fusion studies, image fusion is the integration of different

information sources by taking advantage of the complementary

spatial/spectral resolution characteristics of remote sensing im-

agery. For most earth observation satellites, such as IKONOS,

QuickBird, GeoEye, and WorldView-2, the data provided are

composed of a high spatial resolution (HR) panchromatic (Pan)

image and a low spatial resolution (LR) multispectral (MS)

image. The process of acquiring an HR MS image by blending

an HR Pan image and its corresponding LR MS image is referred

to as “image pan-sharpening.” In practice, images with high

spectral and spatial resolutions are useful in an increasing

number of applications, such as feature detection [2], segmenta-

tion/classiﬁcation [3], [4], and so on.

During the past two decades, a large amount of image fusion

methods have been developed [5]–[7]. In [8] and [9], the

fusion methods are grouped into three categories: 1) projection-

substitution methods, 2) relative spectral contribution methods,

and 3) methods that belong to the Amélioration de la Résolution

Spatiale par Injection de Structures (ARSIS) concept. Projection-

substitution methods, which transform the MS image into an-

other space and exchange one structural component with the Pan

image, are widely used and have been integrated into some

commercial software packages. Among these methods, the most

popular are intensity hue saturation (IHS) transformation [10],

[11], principal component analysis (PCA) [12], and the Gram-

Schmidt transform-based methods [13]. The relative spectral

contribution met hods are based on the assumption that the LR

Pan image can be written as a linear combination of the original

MS image, of which the Brovey transform [14] and the

[15] method are two successful application instances. These two

types of methods can produce a noticeable increase in visual

impression with a good geometrical quality, but a major draw-

back comes from the nonignorable spectral distortion. As for the

ARSIS concept-based methods, it is assumed that the missing

spatial informat ion in the LR MS image can be inferred from the

high frequencies of the HR Pan image. To be speciﬁc, details

extracted from the HR Pan image by certain multi-scale or multi-

resolution decomposition algorithms are injected into the LR MS

image [8], [16]. The signiﬁcant advantage of the ARSIS concept-

based methods is the preservation of the spectral content of the

original MS image. The à trous wavelet pan-sharpening (AWLP)

[17] method and the context-based decision (CBD) [18] method

are two effective ARSIS concept-based methods, which both

lead to good fusion results.

Recently, a new image fusion branch, which transfers the

image fusion problem into an image-related inverse problem

resolved with the help of sparse representation (SR) and com-

pressed sensing (CS) theory, has emerged and shown impressive

fusion performances. Li and Yang [19] wer e the ﬁrst to perfor m

the remote sensing image fusion task from the perspective of CS

[20] theory. Subsequently, Jiang et al. [21] extended the above

model by learning a joint dictionary from the LR MS image and

Pan image to make it more practical. Nevertheless, these CS-

based methods require a large collection of images to train the

dictionary, which is computationally expensive. To deal with this

problem, Li et al. [22] developed a restoration-based remote

sensing image fusion method with sparsity regularization, in

which the dictionary is adaptively learned with the source image.

Manuscript received November 01, 2013; revised January 27, 2014; accepted

February 28, 2014. Date of publication April 03, 2014; date of current version

April 18, 2014. This work was supported in part by the National Basic Research

Program of China (973 Program) under Grant 2011CB707105, in part by the 863

program under Grant 2013AA12A301, and in part by the National Natural

Science Foundation of China under Grant 61201342 and Grant 61261130587.

(Corresponding author: H. Zhang.)

M. Guo, H. Zhang, J. Li, and L. Zhang are with the State Key Laboratory of

Information Engineering in Surveying, Mapping, and Remote Sensing, Wuhan

University, Wuhan 430079, China (e-mail: zhanghongyan@whu.edu.cn).

H. Shen is with the School of Resource and Environmental Science, Wuhan

University, Wuhan 430079, China.

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/JSTARS.2014.2310781

1284 IEEE JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE SENSING, VOL. 7, NO. 4, APRIL 2014

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

With an effective and robust performance, the method still needs

to assume a spectral composition model, which is a little com-

plicated to implement. In [23], Zhu and Bamler proposed an

image fusion method named sparse fusion of images (SparseFI)

which explores the same sparse coefﬁcient vector of the corre-

sponding HR/LR MS image patches over the coupled dictionar-

ies, which are ofﬂine constructed from the Pan image and its

down-sampled LR version. Due to its ease of impleme ntation and

the lack of requirement for external image data, SparseFI has

been considered as a promising approach with a broader appli-

cation range. Recently, a two-step sparse coding strategy for the

pan-sharpening of remote sensing images was proposed in [24]

on the basis of the SparseFI method.

In this paper, we propose an online coupled dictionary learn-

ing (OCDL) approach for image fusion, in which we make full

use of the available LR MS image and the HR Pan image to

decrease the spectral distortion and preserve the spatial informa-

tion of the LR MS image. In the proposed OCDL method, a

superposition strategy is adopted to produce two intermediate

images for the coupled dictionary construction for each band. In

order to ensure that the HR MS image patch can be almost

identically reconstructed by multiplying the HR dictionary and

the same sparse coefﬁcient vector, which is solved by sparsely

representing its counterpart LR MS image patch ov er the LR

dictionary, an iter ative update method is utilized to update the

coupled dictionaries, which can be referred to as an online

dictionary learning process. The theoretical analyses and experi-

mental results in this paper indicate that the proposed method can

produce competitive fusion results, even if the Pan image has a

low correlation with some of the MS bands.

The rest of the paper is structured as follows. Section II brieﬂy

describes SR in ima ge processing a nd the coupled dictionary

model for image fusion. Thereafter, the scheme of the proposed

algorithm is reported in Section III. In Section IV, experiments

with two IKONOS data sets and one WorldView-2 data set verify

the effectiveness of the proposed method, with respect to the

visual, spatial, and spectral quality. Finally, the conclusions are

drawn in Section V.

II. R

ELATED WORKS

A. SR in Image Processing

Sparsity has recently been the subject of intensive research,

and the ﬁeld of ima ge processing has beneﬁtted a lot from the

progress in both theory and practice [25], [26]. In the image

processing approach, each signal R

lexicographically

stacking the pixels can be sparsely represented by

a suitable overcomplete dictionary R

[27], each

column of which corresponds to a possible image patch (also

lexicographically stacking the pixel values in this patch as a

vector). That is to say, signal can be represented as ,

which simultaneously assumes the sparsity of the coefﬁcient

vector . This problem can be formulated as



where 

denotes the number of nonzero components in .

This optimization probl em is NP-hard. It has been shown that

the optimization problem can be converted to an

-norm mini-

mization problem if the desired coefﬁcient  is sufﬁciently

sparse [28], which converts (1) to



A large number of solution algorithms have been developed to

solve the

-norm optimization problem [29], [30], with one of

the classic algorithms being the LASSO algorithm [30].

B. The Coupled Dictionary Model and Its Application

in Image Fusion

The coupled dictionary model was designed to solve the cross-

style image synth esis problem [31], in which each style for the

scene can be mutually transferred by learning the underlying

mapping from the example image pairs. Suppose that we have

some example image pairs from the coupled feature spaces. For

convenience, we assume that the images in one space follow the

style

, and the images in the other space follow style .

The image cross-style synthesis problem can then be formulated

as follows: recover the image in style when its corresponding

description in style is given.

The working mechanism of this model is that there is a

corresponding relationship between the counterpart atoms in

the coupled dictionaries, which leads to a mapping function

between the sparse coefﬁcient vectors of the image patch pairs in

the coupled feature spaces. Clearly, the coupled dictionaries play

an important role in this model. In general, the coupled dict io-

naries are simply generated by randomly sampling raw patches

from the training image pairs of the same scene in the coupled

spaces, or learned from the above raw patch dictionaries. Once

the coupled dictionaries are constructed, each patch of style is

sparsely represented over the dictionary in the space

. The

commonly used and effective mapping function refers to the

assumption that the sparse coefﬁcient vectors in different styles

should be the same, with respect to the delicate coupled dictio-

nary construction [22], [23], [32]. Therefore, the associated patch

of style can be reconstructed with the same sparse coefﬁcient

vector and the dictionary in the space

Image resolution enhancement is one of the classic cross-style

image synthesis problems, where the coupled dictionaries refer

to coupled spaces: the high- and low-resolution signal spaces in

the patch-based SR [32]. Image fusion is a common method of

image resolution enhancement, and the coupled dictionary

model can be used to solve this problem. The SparseFI [23]

method has recently been proposed as an application of the

coupled dictionary model in image fusion. Since an HR Pan

image

and its down -sampled LR version can be directly

utilized, we are able to directly construct the coupled dictionaries

without an extra image data set. In this way, in the SparseFI

method, the coupled dictionaries, which consist of an LR dictio-

nary

and an HR dictionary , are directly constructed from

the Pan image and its down-sampled LR version. To be speciﬁc,

we down-sample the HR Pan image to the same scale as the LR

MS image by using bicubic interpolation, and we then get an LR

Pan image. The LR dictionary

is generated by sampling

raw patches from the LR Pan image with overlapping areas.

GUO et al.: OCDL APPROACH FOR REMOTE SENSING IMAGE FUSION 1285

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