Fusing remote sensing images using à trous wavelet transform and empirical mode decomposition

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1 Available online at Pattern Recognition Letters 29 (2008) Fusing remote sensing images using à trous wavelet transform and empirical mode decomposition Chen Shao-hui *, Su Hongbo, Zhang Renhua, Tian Jing Key Laboratory of Water Cycle and Related Land Surface Processes, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, 11A, Datun Road, Chaoyang District, Beijing, China Received 7 April 2007; received in revised form 11 October 2007 Available online 25 October 2007 Communicated by J.A. Robinson Abstract Á trous wavelet transform (AWT) and empirical mode decomposition (EMD) are two distinct methods used for analyzing nonlinear and nonstationary signals. In this paper, a combination of AWT and EMD is proposed as an improved method for fusing remote sensing images on the basis of the framework of AWT-based image fusion. The principle consists of performing a multiresolution decomposition on high resolution panchromatic image (HRPI) using AWT. The approximation component and low resolution multispectral image (LRMI) are fused through an intrinsic mode functions (IMFs) based model. Subsequently, the sharpening approximation component produced is substituted for the old one. High resolution multispectral image (HRMI) is then obtained through an inverse AWT (IAWT). QuickBird images are used to illustrate the advantage of this method over the traditional AWT and EMD based methods both visually and quantitatively. Ó 2007 Elsevier B.V. All rights reserved. Keywords: Image fusion; Á trous wavelet transform; Empirical mode decomposition; Dyadic wavelet transform 1. Introduction * Corresponding author. Tel.: ; fax: addresses: csh_1976@163.com (S.-h. Chen), hongbo@ieee.org (H. Su), zhangrh@igsnrr.ac.cn (R. Zhang). In optical remote sensing, with technological and physical constraints, satellite sensors cannot supply the images required to distinguish objects both spectrally and spatially (Wang et al., 2005). Many remote sensing applications, such as image analysis, urban mapping and fire monitoring, however require images with simultaneously high spectral and spatial resolution. Theoretically, there exist two approaches to acquire such images. One is to increase the sensitivity of the photo detector of the satellite sensors, but the photons are expensive to collect, making long exposure multispectral observations unusual. Another comes from the field of image fusion, which fuses a high resolution panchromatic image (HRPI) with a low resolution multispectral image (LRMI) of the same scene by applying image fusion algorithms (Núñez et al., 1999). Various remote sensing image fusion algorithms have been proposed. Early methods, such as Brovey transform (Gillespie et al., 1987), principal component analysis (Chavez and Kwarteng, 1989), intensity hue saturation transform (Carper et al., 1990), are mainly focused on intensity modulation for spatial enhancement of multiband LRMIs by means of an HRPI. Although these algorithms yield a good high spatial resolution multispectral image (HRMI) visually, they usually overlook the requirement of the high quality synthesis of spectral information which is crucial for most remote sensing applications based on spectral signatures, such as soil, lithology, and vegetation analysis (Wang et al., 2005). Smoothing Filter based Intensity Modulation (SFIM) method is not applicable for fusing remote sensing images with different illumination and imaging geometry (Liu, 2000) /$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi: /j.patrec

2 S.-h. Chen et al. / Pattern Recognition Letters 29 (2008) Another family of methods on the basis of the injection of high frequency components from the HRPI into the LRMI, such as high pass filtering (Schowengerdt, 1980), ratio of low pass pyramid (Toet et al., 1989), gradient pyramid (Burt and Kolczynski, 1993), morphological pyramid (Matsopoulos et al., 1994), high pass modulation (Schowengerdt, 1997), Laplacian pyramid (Bogoni and Hansen, 2001), provides least spectral distortion than its predecessors. However, it is until the emergence of methods based on multiresolution analysis that the HRMIs accomplish artistic results which can be studied spectrally and spatially (Otazu et al., 2005). According to the algorithm used to decompose the HRPI and the HRMI, these methods can be divided into dyadic wavelet transform (Mallat, 1989), à trous algorithm based wavelet transform (AWT) (Dutilleux, 1989), discrete wavelet frame transform (Unser, 1995), and non-separable wavelet frame transform (Kovačević and Vetterli, 1992). Empirical mode decomposition (EMD) is a recent method for analyzing nonlinear and nonstationary data, which was developed by Huang et al. (1998, 1999). The final representation of signal is an energy frequency distribution, designated as Huang spectrum that gives sharp identifications of salient information. In Section 2, a novel fusion method for enhancing the spatial resolution of an LRMI by means of an HRPI is proposed, based on the joint use of AWT and EMD. We use AWT to separate the low frequency approximation information from the high frequency detail information of the HRPI, and then replace the traditional fusion schemes with EMD for fusing the LRMI and the approximation component of the HRPI. The experimental results presented in Section 3 illustrate that there is consistency between the improvement analysis and the quality report of the fused images. Extensive comparison demonstrates the advantage of the proposed method over the conventional approaches based on the AWT and EMD. The fused images obtained with the proposed method are closer to those observed by the multispectral sensors at the high resolution level. Section 4 concludes the paper. 2. Combined AWT EMD image fusion method AWT can provide good localization in both frequency and space domains in terms of decomposing a signal having finite energy into multiple channels, each one of them with a different degree of resolution (Núñez et al., 1999). The AWT representation of the signal can be obtained by using à trous algorithm (Dutilleux, 1989). EMD is a highly efficient and adaptive method that offers higher frequency resolution and more accurate timing of nonlinear and nonstationary signal events than traditional integral transform techniques (Zhao et al., 2004; Flandrin et al., 2004; Yang et al., 2004). EMD can decompose signal into finite intrinsic mode functions (IMFs), and the sums of all IMFs match the original signal perfectly. More details on the basic theory of EMD can be found in (Huang et al., 1998, 1999). For a two-dimensional image, the EMD process that generates the IMFs is summarized as follows: (1) Treating the original image R as the initial residue r 0. (2) Finding all the local extrema along rows, and then constructing smooth cubic splines connecting all the maxima and minima to get upper envelope ue r and lower envelope le r. Similarly, upper envelope ue c and lower envelope le c along columns are also obtained. The mean plane ul is defined: ul ¼ðue r þ le r þ ue c þ le c Þ=4: ð1þ Then, the difference between r 0 and ul is e 1 ¼ r 0 ul: ð2þ This is one iteration of the sifting process. Generally speaking, e 1 is still a nonstationary series, so this procedure must be repeated until ul is approximately zero. Then e 1 becomes an IMF. The residue is obtained by r 1 ¼ r 0 e 1 : ð3þ (3) Treating the residue as the new input data set. A series of {e i } 16i6I is obtained by repeating (2) until r i is a monotonic function (I denotes the decomposition levels). R can be recovered by inverse EMD (IEMD): R ¼ XI e i þ r I : i¼1 One schematic example of the EMD described above is shown in Fig. 1. The original image is downloaded from The image is decomposed with EMD into two IMFs and one residue. The original image is a synthetic image that contains three kinds of patterns. It is interesting to observe that the two modes and the residue provide very useful information on a series of pattern structures which vary from the smallest to the largest. For an I-level decomposition, the EMD provides a total of coefficients I + 1 times greater than the number of pixels. From the perspective of remote sensing image fusion, the fusion process can be considered as constructing one coefficient with both the same spectral response as the LRMI and the same spatial response as the HRPI at a particular pixel location. With the development of the EMD, we expect much room for improvement over the simple maximum selection and weighted average schemes used to fuse the LRMI and the approximation component of the HRPI. The proposed procedure (Fig. 2) takes the following steps: ð4þ (1) The LRMI is co-registered to the HRPI and resampled to the same pixel size of the HRPI. (2) Decompose the HRPI with AWT to J levels, resulting in a total of J detail components and one approximation component. AWT is used to separate the high frequency textures from the HRPI, and J is determined by the ratio of the resolution of the LRMI to that of the

3 332 S.-h. Chen et al. / Pattern Recognition Letters 29 (2008) Fig. 1. (a) The original image; (b) IMF1; (c) IMF2; (d) the residue. Fig. 2. Schematic diagram of the proposed fusion method. HRPI. Decompose the approximation component and the LRMI by EMD along rows and columns to I levels, resulting in a residue and a total of I IMF planes, respectively. The EMD is completed when the residue, ideally, does not contain any extrema points. For convenience, we first introduce some symbols (Table 1) that will be used in the following text. (3) A good fusion scheme should preserve the spectral characteristics of the LRMI as well as the high spatial resolution characteristics of the HRPI (Wald et al., 1997). In order to inherit the spectral properties of the LRMI, only c I is reserved for IEMD. In order Table 1 Summary of the symbols used Symbol Description x P j P J The wavelet plane of the HRPI at level j The approximation component of the HRPI - P i The IMF plane of the P J at level i - L i The IMF plane of the LRMI at level i c I The residual plane of the LRMI to fuse details from the LRMI and the P J for image enhancement, the IMF plane for the approximation component of the HRMI at level i ð- H i Þ is given by

4 ( - H i ¼ F ð- L i ; -P i Þ¼ -L i ; -P i < - L i ; - P i ; -P i P - L i ; i ¼ 1;...; I: ð5þ (4) Finally, HRMI is recovered by implementing the IEMD and inverse AWT (IAWT) as HRMI ¼ c I þ XI i¼1 - H i þ XJ Compared with the general procedure based on AWT, the proposed procedure has two advantages: (1) only the HRPI is decomposed using AWT until the approximation subband and the LRMI contain features with similar scale, which avoids interscale fusion; (2) the IMF coefficients other than the AWT coefficients are used as the activity level because the IMF coefficients represent further detail information (Nunes et al., 2003; Li et al., 2005; Hariharan et al., 2006). The proposed method can be applied to an arbitrary number of LRMIs. First, the AWT is implemented on the HRPI. The approximation component and the LRMIs are then respectively fused according to the same procedure. Finally, multiband HRMIs can be obtained. 3. Experiments j¼1 S.-h. Chen et al. / Pattern Recognition Letters 29 (2008) x P j ð6þ AWD method to perform the whole fusion procedure on a 3 GHz Pentium double CPU personal computer. The other fusion methods based on the AWT and the EMD are also implemented. For the AWT and EMD, à trous filter 2 1/2 (1/16, 1/4,3/8, 1/4,1/16), together with a decomposition level of two, and cubic spline function, a decomposition level of three, coefficient based activity, and choose max scheme are used. Fused images (HRMIs) using different algorithms are shown in Fig. 3c e. Since the HRMIs are too large to be assessed together, for better evaluation, Fig. 4 shows subscenes of size from the LRMIs and the corresponding HRMIs. The performance of each fusion method is estimated by comparing the fused images in terms of the quality of the synthesis of both spatial and spectral information, which means that the HRMIs should be as identical as possible to the real HRMIs (RHRMIs) the corresponding multispectral sensor would observe if it worked at the spatial resolution of the HRPI (Wang et al., 2005; Otazu et al., 2005). In order to evaluate the quality of the fused images, they should be compared with the RH-RMIs the QuickBird multispectral sensor would collect at the spatial resolution of 0.7 m. Since the RHRMIs do not exist in practice, Wald s protocol (2000) is employed for the quantitative evaluation. Visual inspection is an effective tool for analyzing the major advantages and disadvantages of a method, and is used for the qualitative evaluation. The raw images are downloaded from These images are acquired by a commercial satellite, QuickBird, which collects one 0.7 m resolution panchromatic band ( nm) and blue ( nm), green ( nm), red ( nm), near infrared ( nm) bands of 2.8 m resolution. The QuickBird data set was taken over the Pyramid area of Egypt in The test images of size 1024 by 1024 at the resolution of 0.7 m are cut from the raw images and used as HRPI and LRMIs. Fig. 3a displays the LRMIs as a color composite where the red, green, blue bands are mapped into the RGB color space. The HRPI is shown in Fig. 3b. The near infrared band is not shown because of the limited space in this paper, although the images were processed and numerically evaluated. The study area is composed of various features such as roads, buildings, trees, etc., ranging in size from less than 5 m up to 50 m. It is obvious that the HRPI has better spatial resolution than the LRMIs and more details can be found from the HRPI. Before the image fusion, the raw LRMIs were resampled to the same pixel size of the HRPI in order to perform image registration. The resolution ratio between the QuickBird HRPI and the LRMIs is 1:4. Therefore, when performing the proposed fusion algorithm termed AWD, for the AWT, à trous filter 2 1/2 (1/16,1/4,3/8,1/4,1/16), together with a decomposition level of two, is employed to abstract the high frequency information of the HRPI. For the EMD, cubic spline function, along with two levels of decomposition, is used. It will take approximately s for the 3.1. Visual inspection Visual inspection provides a comprehensive impression of image clarity and the similarity of the original and fused images (Wang et al., 2005). By visually comparing all the HRMIs (Fig. 3c e) with the LRMI (Fig. 3a), it is apparent that the spatial resolutions of the HRMIs are much higher than that of the LRMI. Some small spatial structure details, such as edges, lines, which are not discernible in the LRMI, can be identified individually in each of the HRMIs. Buildings corners, holes, and textures are much sharper in Fig. 3c e than in Fig. 3a and can be seen as clear as in Fig. 3b. This means that all of the fusion methods can improve the spatial quality of the LRMI during the fusion process. It can be seen from Fig. 3c and d that the HRMIs produced by AWT and EMD display slight color distortion. A general appearance is that in Fig. 3c and d, the color of the slope area is deflected from light purple to green purple and deep purple, respectively. 1 It is easy to see this effect in Fig. 4 by enlarging a region of interest. For AWT, this is probably due to over enhancement along the edge area because the AWT method has not considered the differences in high frequency information between the LRMI and the approximation component of the HRPI (Wang et al., 2005). For EMD, it is difficult to well define the 1 For interpretation of color in Fig. 3, the reader is referred to the web version of this article.

5 334 S.-h. Chen et al. / Pattern Recognition Letters 29 (2008) regional extrema (the saddle points of edges and building corners) before the AWT decomposition, and the influence is not negligible in this case. It is clear to see that the HRMI (Fig. 3e) from AWD appears the best among all the HRMIs. The color is almost not distorted, and the integration of spatial features and color is natural. These show that the AWD method ensures the preservation of the spectral information of the LRMI when increasing its spatial information. For the AWD, the IMF coefficients bring not only sharp localization of details but also sharp frequency (Nunes et al., 2003); as a result, better HRMI can be obtained. Overall, it is obvious by visual analysis that the AWD method gives the HRMI closest to what the multispectral sensor would observe at the spatial resolution of the HRPI Quantitative comparison In addition to the visual inspection, the performance of each method is further quantitatively analyzed by checking Wald s protocol. Since the RHRMIs do not exist, the original LRMIs are treated as the RHRMIs to compare with the HRMIs from integrating the original LRMIs and HRPI, or the spatially degraded LRMIs and HRPI. Fig. 3. (a) LRMIs at 2.8 m resolution level. (b) HRPI at 0.7 m resolution level. (c) AWT HRMIs at 0.7 m resolution level. (d) EMD HRMIs at 0.7 m resolution level. (e) AWD HRMIs at 0.7 m resolution level. (f) NIR LRMI at 2.8 m resolution level. (g) AWT NIR HRMI at 0.7 m resolution level. (h) EMD NIR HRMI at 0.7 m resolution level. (i) AWD NIR HRMI at 0.7 m resolution level. (j) Degraded AWT HRMIs at 2.8 m resolution level. (k) Degraded EMD HRMIs at 2.8 m resolution level. (l) Degraded AWD HRMIs at 2.8 m resolution level. (m) Degraded AWT NIR HRMI at 2.8 m resolution level. (n) Degraded EMD NIR HRMI at 2.8 m resolution level. (o) Degraded AWD NIR HRMI at 2.8 m resolution level.

6 S.-h. Chen et al. / Pattern Recognition Letters 29 (2008) Fig. 3 (continued) Spectral quality of the fused HRMIs is estimated using the following quantitative indicators (Wald, 2000). (1) Correlation coefficient (CC) between each band of the original multispectral and the fused image. It should be as close to 1 as possible. (2) Root mean square error (RMSE) between each band of the original and the fused image, computed using the following equation: RMSE 2 ¼ bias 2 þ SDD 2 ; ð7þ where the bias is the difference between the mean value of the original and the fused image and SDD the standard deviation of the difference image between the original and the fused image. RMSE should be as close to 0 as possible. (3) Spectral angle mapper (SAM) (Alparone et al., 2004) between each band of the original multispectral and the fused image, defined as P n i¼1 SAM ¼ arccos u iv i pffiffiffiffiffiffiffiffiffiffiffiffiffiffi P n p ffiffiffiffiffiffiffiffiffiffiffiffiffiffi P n ; ð8þ i¼1 u2 i i¼1 v2 i where u =(u 1,u 2,...,u n ) and v =(v 1,v 2,...,v n ) denote the spectral vectors of the original and fused band. It should be as close to 0 as possible.these parameters only allow estimating the difference in spectral content between corresponding bands of the original and fused images. In order to estimate the global

7 336 S.-h. Chen et al. / Pattern Recognition Letters 29 (2008) spectral quality of the fused images, the following indicators are used. (4) Relative average spectral error (RASE) characterizes the average performance of the image fusion method in the spectral bands considered RASE ¼ 100 M vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 1 X t N RMSE 2 ðb i Þ; ð9þ N i¼1 where M is the mean radiance of the N multispectral bands (B i ). RASE should be as close to 0 as possible. (5) Erreur relative globale adimensionnelle de synthèse (ERGAS), whose english translation is relative dimensionless global error in fusion (Wald, 2000), given by vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ERGAS ¼ 100 h u 1 X t N RMSE 2 ðb i Þ ; ð10þ l N i¼1 where h is the resolution of the HRPI, l the resolution of the LRMI, N the number of spectral bands (B i ) involved in the fusion, and M i the mean radiance of each spectral band. ERGAS should be as close to 0 as possible. M 2 i Fig. 3 (continued)

8 S.-h. Chen et al. / Pattern Recognition Letters 29 (2008) Fig. 3 (continued) (6) The universal image quality (UIQ) index (Wang and Bovik, 2002) models the difference between two images as a combination of three different factors: loss of correlation, radiometric distortion, and contrast distortion. The dynamic range of UIQ is [ 1,1]. If two images are identical, the similarity equals 1 UIQ ¼ r AB 2l A l B 2r A r B r A r B l 2 A þ l2 B r 2 A þ ; ð11þ r2 B where l A and l B are the mean of the original (A) and fused (B) image; r A and r B are the standard deviations of A and B; r AB is the covariance between A and B. The UIQ index is usually calculated using a sliding window approach. In this work, sliding windows with a size of 16 16, 32 32, 64 64, and pixels are used. Considering that the UIQ index can only be applied to monochromatic images, the average value (Q avg ) is used as a global spectral quality index for multispectral images. The higher the Q avg value the higher the spectral and radiometric quality of the fused image (Otazu et al., 2005). In order to test the first property of Wald s protocol, the fused HRMIs are spatially degraded to the resolution level of the original LRMIs (2.8 m) by box interpolation. Then these indicators are computed between the degraded HRMIs and the original LRMIs at the 2.8 m resolution

9 338 S.-h. Chen et al. / Pattern Recognition Letters 29 (2008) Fig. 4. (a) Subscene of the LRMIs at 2.8 m resolution level. (b) Subscene of the AWT LRMIs at 2.8 m resolution level. (c) Subscene of the EMD LRMIs at 2.8 m resolution level. (d) Subscene of the AWD LRMIs at 2.8 m resolution level. Table 2 Values of the different indicators analyzed to evaluate the quality of the fused images at 2.8 m resolution level (fusion at the original level) Band AWT EMD AWD Ideal CC B B B B RMSE B B B B SAM B B B B Q avg Q avg Q avg Q avg RASE ERGAS Table 3 Values of the different indicators analyzed to evaluate the quality of the fused images at 2.8 m resolution level (fusion at the inferior level) Band AWT EMD AWD Ideal CC B B B B RMSE B B B B SAM B B B B Q avg Q avg Q avg Q avg RASE ERGAS

10 S.-h. Chen et al. / Pattern Recognition Letters 29 (2008) level. In Table 2, the last column reflects the situation that should be ideally reached after the fusion process. For convenience, let B 1, B 2, B 3, and B 4 represent the red, green, blue, and near infrared bands, respectively. It can be seen from Table 2 that all methods allow a high quality transformation of the multispectral information when increasing the spatial resolution of the LRMI. The degree of similarity between the LRMI and the HRMI corresponds to the degree of spectral distortion of each method. The lower the similarity between the LRMI and the HRMI, the higher the spectral distortion, and vice versa. Table 2 shows that each value of the AWD method is the best among all the fusion methods. Therefore, we can draw a conclusion that the AWD method has the least color distortion. The AWT method has slight color distortion. The EMD method has the largest color distortion. What is more, these statistical assessment results agree with those of the visual inspection. In order to test the second and third properties, the LRMIs and HRPI are respectively degraded to 11.2 m pixel size and 2.8 m pixel size by box interpolation. Then each image fusion method is applied to the degraded data to yield the degraded HRMIs at 2.8 m resolution level, Fig. 5. (a) Origianl LRMIs at 2.8 m resolution level. (b) Degraded LRMIs at 11.2 m resolution level. (c) Degraded HRPI at 2.8 m resolution level. (d) Original NIR LRMI at 2.8 m resolution level. (e) Degraded NIR LRMI at 11.2 m resolution level. (f) Degraded AWT HRMIs at 2.8 m resolution level. (g) Degraded EMD LRMIs at 2.8 m resolution level. (h) Degraded AWD HRMIs at 2.8 m resolution level. (i) Degraded AWT NIR HRMI at 2.8 m resolution level. (j) Degraded EMD NIR HRMI at 2.8 m resolution level. (k) Degraded AWD NIR HRMI at 2.8 m resolution level.

11 340 S.-h. Chen et al. / Pattern Recognition Letters 29 (2008) Fig. 5 (continued) after which the degraded HRMIs are assessed against the original LRMIs at the 2.8 m resolution. Table 3 shows the results (see Fig. 5). From Table 3, all of the fusion methods yield high scores for the four bands and the difference is very small. As a whole, the AWT method produces less color distortion than the EMD method, which is also consistent with the conclusion from Table 2. The AWD method gives the best scores for the four bands. This is probably because the spatial degradation process will influence the final result differently for different fusion method. However, the quality of the HRMIs at the original resolution level cannot be predicted from the assessments at the inferior level (Wang et al., 2005). The AWD method gets the advantage of the AWT and EMD methods in fusing remote sensing images, because the injection model incorporates spatial details of the HRPI into each band of the LRMIs by taking into account both information separation, as is the case of the AWT decomposition process, and pixel spectral signature, as is the case of the EMD transformation. This procedure allows producing HRMIs closer to the RHRMIs that the multispectral sensor would take at the spatial resolution of the HRPI. By combining the visual inspection results and the quantitative comparison, it can be seen that the AWD method gives the HRMIs closer to the RHRMIs than the EMD and AWT methods when the HRMIs are compared with the original LRMIs and the HRPI.

12 S.-h. Chen et al. / Pattern Recognition Letters 29 (2008) Fig. 5 (continued) 4. Conclusions In this paper, we study the hybrid of AWT and EMD for fusing LRMI and HRPI of the same scene in order to obtain HRMI. AWT is used for decomposing the HRPI into a series of wavelet planes and one approximation component, while EMD is used for decomposing the approximation component and the LRMI into IMFs and residues. Then, the LRMI and the approximation subband are fused based on the IMFs determining which one has the better spatial and spectral responses at a given pixel position. QuickBird LRMIs and HRPI are fused to evaluate our proposed method. The results are compared with those of the traditional AWT and EMD methods by visual inspection and statistical analyses. The inter-comparison results confirm the spectral preservation property of the proposed method. Compared with the separate AWT and EMD methods, the proposed method is more computational intensive when implemented to perform real-time image fusion on-the-fly. Overall evaluation of the hybrid method of AWT and EMD shows that it is a promising method and superior to previous AWT and EMD separately. References Alparone, L., Baronti, S., Garzelli, A., Nencini, F., Landsat ETM+ and SAR image fusion based on generalized intensity modulation. IEEE Trans. Geosci. Remote Sens. 42 (12),

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