8/2/2019 04721823

1/4

A Remote Sensing Image Fusion Algorithm Based on

Nonnegative Ordinal Independent ComponentAnalysis by Using Lagrange Algorithm

Zhongni Wang, Xianchuan Yu*, Wang YuDai Sha

College of Information Science and Technology

Beijing Normal University

Beijing, 100875, China{Chuan.yu@ieee.org, bameinini@163.com}

Abstract Data fusion on remote sensing is one of important

problems in current image processing. The key of a successful

image fusion is to find an effective and practical image fusionalgorithm. To eliminate high-order image data redundancy for

two different remote sensing images which is nonnegative, a new

approach using the nonnegative ordinal independent component

analysis(ICA) based on Lagrange algorithm for remote image

fusion between panchromatic and multi-spectral images is

proposed. Firstly, the multi-spectral image and the panchromatic

image are registered with the error in a pixel. Then the

independent components, obtained by nonnegative ICA

transform, are done factor analysis to determine the sequence of

independent components successfully. Finally, the fused image is

obtained by applying image fusion rules. Visual and statistical

analyses prove that the concept of fusion method based on

nonnegative ordinal ICA is promising, and it does significantly

improve the fusion quality with higher signal-to-noise ratio

compared to conventional IHS and wavelet fusion techniques.

Keywords-Image fusion; Independent Component Analysis;

Factor Analysis; Remote sensing image

I. INTRODUCTION

With the development of modern remote sensingtechnology, the spatial and spectral resolution of remotesensors has been greatly improved which leads to the diversityand complexity of data sources. The data fusion is an importanttool for improving the data quality in remote sensing and caneffectively integrate the images from different sources into oneimage. The image fusion techniques have become a hotproblem in recent years [1-5].

Because of the importance of image fusion techniques,

many image fusion algorithms have been proposed. Traditionalimage fusion methods in the remote sensing contain theintensity-hue-saturation (IHS) transform, principal componentanalysis (PCA), discrete wavelet transform (DWT) and etc. [6].Although these methods improve the quality of the fusionresult, there are still some limitations. For example, thesefusion algorithms do not eliminate redundancy betweendifferent data, or just eliminate the low-order data redundancy,and do not consider the higher-order statistical properties of thesignal [7].

In this paper, to overcome these limitations, we propose anew image fusion algorithm for Landsat ETM+ and CBERS

images. The new fusion method is Nonnegative ordinalIndependent Component Analysis based on Lagrange

Algorithm LNO-ICA . Experimental comparison withconventional fusion methods shows that the LNO-ICA fusionmethod outperforms these existing approaches

II. NONNEGATIVE INDEPENDENTCOMPONENT ANALYSIS

The traditional fusion methods including IHS, PCA andDWT are all based on spatial or frequency domain which doesnot consider redundancy between the different signals.Although the PCA method could eliminate the low-orderredundancy, it does not take the high-order redundancy intoconsider. According to the statistical theory, the most importantinformation of image signal is always included in the statistical

characteristics of high-order [8]. Independent componentanalysis which is recently developed from blind sourceseparation is a novel high-order statistic signal processingmethod and it tries to transform an observed multidimensionalvector into components that are statistically as independentfrom each other as possible [9-13]. ICA is very useful andgradually become a hot problem in signal processing. RecentlyICA is widely applied in biomedicine signal processing, soundsignal separation, communication, error diagnose, featureextraction, financial time sequence analysis, data mining,image processing and etc.

A. Independent component analysisICA is signal processing technique whose goal is to express

a set of random variables as linear combinations of statistically

independent component variables. The estimation of the datamodel of independent component analysis is usually performed by formulating an objective function and then minimizing ormaximizing it. Therefore, the properties of the ICA methoddepend on both of the objective function and the optimizationalgorithm. Assume that there is an M-dimensional zero mean

vector1 2

( , ,..., )TM

s s s s= , whose components are mutually

independent. The vector ( )s t corresponds to n independent

scalar valued source signali

s . We can write the multivariate

2008 International Conference on Computer Science and Software Engineering

978-0-7695-3336-0/08 $25.00 2008 IEEE

DOI 10.1109/CSSE.2008.1380

610

8/2/2019 04721823

2/4

p.d.f. of the vector as the product of marginal independentdistributions.

( ) ( ) (1)M

i i

i

p s p s=

A data vector 1 2( , ,..., )N

Tx x x x= is observed vector at

pointt, such that

( ) ( ) (2)x t As t =

Where, A is an N*M scalar matrix which is called mixingmatrix.

Sometimes we need the columns of matrix A, if we denote

them byj

a the model can also be written as,

1

(3)n

i i

i

x a s=

=

The goal of ICA is to find a linear transformation Wof the

correlative signals that makes the outputs as independent aspossible:

( ) ( ) ( ) (4)u t W x t W As t = =

Where, u is an estimate of the sources. Intuitively speaking,the key to estimating the ICA model is non-Gaussianity. It ismainly because the non-Gaussian means independent.

The estimation of data model of independent componentanalysis usually chooses a suitable objection function and thenminimizes or maximizes it. It means that an ICA methoddepends on objection function and optimization algorithm.

B. Nonnegative independent component analysisAs the ICA methods can not ensure that the independent

components are nonnegative, but the remote image data isnonnegative. Several authors have introduced some algorithmsfor nonnegative ICA [14], yet these algorithms are all based onthe assumption that the sources are well-grounded except forindependence and nonnegative. We propose a new remotesensing image fusion algorithm based on nonnegativeindependent component analysis by using Lagrange arithmeticeven in the case that the sources are not well-grounded. We

choose the Kurtosis( )kurt u

as the objection function.

4 2 2( ) ( ) [( ) ] 3{ [( ) ]} (5)T T Tkurt u kurt w x E w x E w x= =

With the constraint of 0Tu w x= , the objection function

is as follows,

( ( )) ( ( ))(6)

0

T

T

Max kurt u Max kurt w x

u w x

=

=

We can use the Lagrange multipliers method to solve the

problem, we assume the ij is Lagrange multipliers

corresponding to the condition of 0Tu w x= , denoting

by [ ]ij = ,

( ) ( ) ( ) ( ) (7)T TL kurt u tr u kurt w x tr w x = + = +

Then doing partial derivative of L within Kuhn-Tuckerconditions, the issues could be solving by following equations,

34 [ ( ) ] 3 0 (8)

0 (9)

T

T

LE x w x w x

w

w x

= + =

=

As the equation is non-homogeneous, there is no generalsolution for the equation. The both sides of equation (10) are

multiplied by w , and then the iteration is as follows,

34 [ ( ) ]

(10)3

TE x w x

w

C. Factor AnalysisIn the ICA model, it is easy to see that we cannot determine

the order of the independent components.

The reason is that, again both s and A being unknown inequation.

1( )( ) (11)i i i

i i

x A s a s bb

= =

We can freely change the order of the terms in the sum andcall any of the independent components the first one. Formally,a permutation matrix P and its inverse can be substituted in the

model to give -1x AP Ps= . The elements ofPs are the original

independent variablesj

s , but in another order. The matrix-1

AP is just a new unknown mixing matrix, to be solved by theICA algorithms.

However, the ambiguity of the independent componentssequence has not been concerned. This is mainly because theICA method was applied to different kinds of blind sourceseparation problem. The uncertainty of the independentcomponents sequence did not have an impact on the solution ofthe issue in several fields. However, when dealing with mineralresources prediction, the sequence of independent components(ICs) is quite important to explain the results. Therefore, theordinal ICA algorithm uses factor analysis methods to obtain

unique ICs.

The basic idea of factor analysis is group by the correlationof variable, so that the variable in the same group has highercorrelation, but in different group with lower correlation. Eachgroup represents a basic structure, are called factor.

611

8/2/2019 04721823

3/4

Assume a random vectorx with p dimension, the mean ofit is, covariance is . The factor analysis model is as (12).

( 1 2 )X L f = + +

Where1 2, ,...

mf f f is mutual factors and 1 2, ,... p is

specific factors or error, ( )ij p m

L l

= , The elementsij

l of

matrix L are called factor loadings.

To establish factor model, first we should estimate factorloadings matrix and special variance. The common methods ofparameter estimation has been used in such techniques as PCAmethod, the main factor method, the maximum likelihoodmethod and etc.. Then, look for a reasonable interpretation ofthe factors. To reduce subjectivity of the interpretation, factorrotation is introduced. Therefore, the results are then easier tointerpret. We use the varimax as the factor rotations technique.

Therefore, to revert the corresponding original signals, wedo factor analysis and see the mixed and independentcomponents as new observed data. The two components whichcontribute most to the same common factor can be seemed as

the corresponding components.

III. REMOTE SENSING IMAGE FUSION BASED ON LNO-ICA

To eliminate high-order image data redundancy for twodifferent Remote sensing images, we introduce LNO-ICA forremote image fusion between Landsat ETM+ panchromaticand CBERS multi-spectral images. The images after LNO-ICAas a new tool for image fusion both could improve spatialresolution and preserve spectral characteristics.

The study area is located in the urban area of Zhuhai,China. Figure1(a) shows a CBERS multi-spectra image with bands 4, 3 and 2, acquired in 2001.Figure 1(b) shows theETM+ panchromatic image, acquired in 2001.A scene of 256 256 pixels in size was selected for our experiments, and it

includes some ground covers, such as the area for agriculture,forest, grass, man-made infrastructure and etc. Before theimage fusion, the multi-spectral images were co-registered tothe corresponding panchromatic images.

In our experiment, as the resolution of images is 256 256.We can see the multi-spectra image with bands 4, 3 and 2andpanchromatic image as a random matrix of (256 256) 4, so

that the observed signal is [ , , , ]TV R G B P = , here, R, G, B

(a)

(b)Figure 1. Multi-spectral image and panchromatic image (a)

original CBERS multi-spectral image with bands 1, 2 and 3; (b) OriginalETM+ panchromatic image

respectively corresponding to the three bands of multi-spectralimage, P stands for the panchromatic image. So each column of

matrix V stands for a picture. The figure 2 is the images withthree different bands corresponding to the figure1 (a).

(a) Band 4 (b) Band 3 (c) Band 2Figure2. the 3 bands of Multi-spectral image

The detailed steps of this integrated fusion method are asfollows, first, registering the multi-spectral image and the panchromatic image with the error in a pixel, and denoting

by [ , , , ]T

x R G B P = . Then we obtain the independent

components by nonnegative ICA, with it denoting by

1 2 3[ , ]Ts 4= , , .therefore, we have a new matrix owned 8vectors. The former four vectors are observed signals

[ , , , ]Tx R G B P = and the latter four vectors are independent

components 1 2 3[ , ]Ts

4= , , . As the factor analysis can

eliminate indeterminacy of ICA results, we do factor analysisto get 4 common factors. Next, find an effective fusion rule forfusion. The detailed fusion rule is as follows:

1 1 4( ) / 2 ( 1 3 ) +=

2 2 4( ) / 2 (1 4 ) +=

3 3 4( ) / 2 (1 5 ) = +

Where, we assume the independent components

1 2 3 4 are the estimate of observed signals

[ , , , ]Tx R G B P =sequentially. At last, the fusion image is

obtained.

612

8/2/2019 04721823

4/4

IV. EXPERIMENTSANDEVALUATION

Before the image fusion, the multi-spectral images were co-registered to the corresponding panchromatic images.Experimental results compared with those of conventionalfusion methods including IHS [15], PCA [16] and DWT [17]are shown in figure 3.

(a) I HS (b) DWT

(c) PCA (d) LNO-ICAFigure 3. the fused results: (a) I HS; (b) DWT; (c) PCA; (d) LNO-ICA

To assess the quality of the fused images, this experimentaluse the signal-to-noise ratio (PSNR) as statistical parameter toevaluate the effect fusion result. The quantitative results ofdifferent fusion method are shown in table 1.

TABLE I. THE CONTRAST OF PSNR

The PSNR is used to measure the difference betweenimages. By analyzing and comparing the all fusion methodsfrom statistical parameters (table 1) and visual measurements(Fig. 3), we can draw conclusions that, the LNO-ICA fusionmethod produce better result with higher PSNR. From visualmeasurements aspect (Fig. 3), the same conclusion can bedrawn. In other words, the images after LNO-ICA as a newtool for image fusion both could improve the quality of fusionimage.

V. CONCLUDINGREMARKS

ICA is a novel method for finding underlying componentsfrom multivariate statistical data and gradually become a hot

problem in signal processing. To eliminate high-order imagedata redundancy for two different remote sensing images, we

propose a new method that is LNO-ICA for remote image

fusion between Landsat ETM+ panchromatic and CBERSmulti-spectral images. At the same time, we use factor analysisto determine the sequence of ICA results. After applying theeffective fusion rule, we can get more exact results.Experiments show that compared with those of conventionalmethods, LNO-ICA fusion method produces better fusionresult.

VI. ACKNOWLEDGEMENTS

This paper is supported by the National Natural ScienceFoundation of China (No. 60602035, 40372129), NaturalScience Foundation of Beijing (No. 4062020) and program for

New Century Excellent Talents in UniversityNCET-06-0131

.Thanks for the data supplier Wang Shan in Beijing Normal

University.

VII. REFERENCES

[1] Mitianoudis N, Stathaki T. Pixel-based and region-based image fusionschemes using ICA bases [J].Information Fusion, 2007, 8(2),pp.131142.

[2] Pohl C, Van Genderen J L. Multi-sensor image fusion in remote sensing:concept, methods and applications [J]. International Journal of Remote

Sensing, 1998, 19(5),pp.823854.[3] Cardinali A, Nason G P. A Statistical Multiscale Approach to Image

Segmentation and Fusion[C]. Philadelphia: 8th International Conferenceon Information Fusion, 2005,pp.475482.

[4] Huang xin,Zhang liang pei,Li ping xiang.Classification of High SpatialResolution Remotely Sensed Imagery Based Upon Fusion of MultiscaleFeatures and SVM [J].Journal of Remote Sensing, 2007, 01,pp.48-54.

[5] Zhang Yun, Hong Gang. An IHS and wavelet integrated approach toimprove pan-sharpening visual quality of natural Color IKONOS andQuickBird images [J].Information Fusion, 2005, 6,pp.225234.

[6] Yang Rongling, Ehlers M., Usery E.L., et al. FFT-enhanced IHStransforms method for fusing high-resolution satellite images [J]. Journalof Photogrammetry and Remote Sensing, 2007,pp. 381392.

[7] Nikolaos Mitianoudis, Tania Stathaki. Pixel-based and region-basedimage fusion schemes using ICA bases [J]. Information Fusion, 2007,8(2),pp.131142.

[8] Hyvrinen A, Hoyer P O, Inki M. Topographic Independent Component

Analysis [J], Neural Computation, 2001, 13,pp.15271558.

[9] M. Chen, J. H. Xuan, D. R. Li, Q. Q. Qin, Y.H. Jia, Image FusionAlgorithm Based on Independent Component Analysis, Opto-Electronic Engineering, vol.34,pp.82-87, 2007.

[10] Mitianoudis N., Stathaki T. Adaptive Image Fusion Using Ica Bases[C].Toulouse, Acoustics, Speech and Signal Processing, 2006.

[11] Hyvrinen A, Oja E. Independent component analysisAlgorithm andapplications [J].Neural Networks, 2000, 13(4),pp.411430.

[12] Jutten C, Herauh J. Blind separation of sourcesPart I:An adaptivealgorithm based on neuromimatic architecture [J].Signal Processing1991, 24(1),pp.110.

[13] Comon P. Independent component analysis, a new concept? [J], SignalProcessing, 1994, 36,pp.287314.

[14] Plumbley M D.Condition for nonnegative independent componentanalysis [J], IEEE Signal Processing Letter, 2002, 9,pp.177~180.

[15] Chen Huaixin. A Multi-resolution Image Fusion Based on PrincipleComponent Analysis[C]. Chengdu: Fourth International Conference onImage and Graphics, 2007.

[16] Choi M A. New Intensity-Hue-Saturation Fusion Approach to ImageFusion with a Tradeoff Parameter[J]. IEEE Transactions on Geoscienceand Remote Sensing, 2006, 44(6),pp.16721682.

[17] Zhou J, Civco D L, Silande J A. A wavelet transform method to mergeLandsat TM and SPOT panchromatic data [J], International Journal ofRemote Sensing, 1998, 19 (4),pp.743757.

Band

PSNR

IHS DWT PCA LNO-ICA

R 14.5890 16.4525 11.3327 20.9196

G 13.8819 15.3591 11.3741 19.9235

B 13.8548 15.0530 11.4700 20.0556

613