Pan-Sharpening Using an Adaptive Linear Model - Semantic Scholar
2010 International Conference on Pattern Recognition
Pan-Sharpening Using an Adaptive Linear Model Lining Liu1 , Yiding Wang2 , Yunhong Wang1 , Haiyan Yu1 1. School of Computer Science and Engineering, Beihang University, Beijing, China 2. College of Information Engineering, North China University of Technology, Beijing, China lining [email protected], [email protected] [email protected], [email protected]
Abstract In this paper, we propose an algorithm to synthesize high-resolution multispectral images by fusing panchromatic (Pan) images and multispectral (MS) images. The algorithm is based on an adaptive linear model, which is automatically estimated by least square fitting. In this model, a virtual difference band is appended to the MS to guarantee the correlation between the Pan and MS. Then, an iterative procedure is carried out to generate the fused images using steepest descent method. The efficiency of the presented technique is tested by performing pan-sharpening of IKONOS, QuickBird, and Landsat-7 ETM+ datasets. Experimental results show that our method provides better fusion results than other methods.
1. Introduction Due to the inverse relationship between the spectral and spatial resolutions in sensor design [8], most spaceborne optical sensors, such as Landsat, SPOT, IKONOS and QuickBird, provide two different kinds of data, high spectral resolution images at low spatial resolution and high spatial resolution images at low spectral resolution. Many works have demonstrated the benefits of fusing the multispectral (MS) images and panchromatic (Pan) images in land mapping applications [6]. The fusion technique, known as pan-sharpening, has been an active area in the last decade, and many pansharpening methods have been developed [9]. Existing pan-sharpening methods can be categorized into two groups. One is based on the linear correlation between Pan and MS, such as principal component analysis (PCA) based methods, intensity hue saturation (IHS) transform based methods [10], Brovey transform method, and P+XS method [2]. This kind of methods can produce good visual results in most cases, but spec1051-4651/10 $26.00 © 2010 IEEE DOI 10.1109/ICPR.2010.1096
tral distortion is unavoidable for its dependence on the linear relation between Pan and MS. In fact, this relation is certainly not linear. The other is based on multiresolution or multiscale analysis algorithms like wavelet based methods, Gram-Schmidt method [5], and ARSIS (Amlioration de la Rsolution Spatiale par Injection de Structures) concept methods [7]. Results with better spectral quality can be provided by multiscale-based methods, but it has been demonstrated by several experiments that these methods may cause local heterogeneity and degrade the quality of the result [9]. In this paper, we propose a pan-sharpening method based on an adaptive linear model, in which a virtual difference band is appended to the original MS to generate the linear relation between Pan and appended MS. The synthetic high-resolution multispectral image is generated by an iterative algorithm based on steepest descent method (SDM). Compared with existing techniques, the spectral distortion is decreased significantly and the good geometrical quality is achieved.
2. The adaptive linear model For the first kind of pan-sharpening methods introduced in Section 1, it is assumed that Pan equals the linear combination of bands in MS. But the unfitness between real data and the model causes the spectral distortion in pan-sharpening. If we introduce the difference between Pan and the linear combination of MS bands, the relation between Pan and MS would be modeled well. In our fusion framework, the model is presented as Equation (1): P = α0 +
N ∑
αi Bi + Bd ,
(1)
i=1
where P is Pan, αi is the weight of the ith band Bi of MS, and α0 is the constant part of the difference. Bd is the variant part. The difference items ensure that the 4492 4520 4512
preserve the spectral information. So the convergence of the algorithm is determined not only by minimizing E but also by preserving Bd . The whole pan-sharpening algorithm is an iterative optimizing procedure, described as follows: 1. Coefficient matrix A, difference band Bd and MS+ are calculated as the algorithm designed in Section 2. 2. MS+ is expanded to the same size of Pan, and the expanded MS+ is treated as the initial value of the (0) synthetic high-resolution multispectral image M S+h . (q) 3. The pixel value of each band in M S+h is updated as follows:
Equation (1) is tenable, if the relation between Pan and MS is not linear. Whether the Pan-MS pair is in high or low resolution, this model should the same. For the original MS, Bd can be derived as follows: 1. P is resampled to the size of MS to obtain lowresolution Pan Pl ; 2. Coefficient matrix A = [α0 , α1 , · · · , αN ]T is solved using least square fitting method. Define matrixes Y, and X: [ ]T Y = Pl1 Pl2 · · · Plm · · · PlM , 1 B11 · · · Bi1 · · · BN 1 .. .. .. .. . . . . Bim BN m X = 1 B1m . .. .. .. .. . . . 1 B1M · · · · · · · · · BN M where M denotes the number of pixel in MS, m is the index number of pixel in MS and Pan. A = (X T X)−1 X T Y.
(n+1)
Bik
(2)
K ∑ ∂E ∂Bik |Bk =Bk(n) < ε1 ,
(3)
If d(q) − d(q−1) < ε2 , ε2 is a small positive number, the convergence of our algorithm is reached; else the (q) N + 1th band of M S+h is substituted by expanded (q+1) Bd to get M S+h , and return to step 3. 6. The synthetic high-resolution MS is generated by (q) extracting the former N bands from M S+h . It should be noted that the bilinear interpolation is adapted in all resampling processing. The selection of parameters λ, ε1 , ε2 effects the number of iteration and the result’s quality. It’s necessary to set appropriate values to them. λε1 /K should be less than 0.1. ε2 is suggested to be less than 2.
The steepest descent method is a first-order optimization algorithm, which can be represented as Equation (4),(5). minf (x), x ∈ Rn , (4) (5)
SDM has been adopted for pan-sharpening in [2][4]. In our pan-sharpening algorithm, the object function is defined as Equation (6): K ∑ k=1
(α0 +
N ∑
αi Bik + Bdk − Pk )2 ,
(8)
where minimum energy change ε1 is a small positive number. 5. The root mean square error (RMSE) between the (q) degraded N +1th band of M S+h and Bd is calculated as: v u M u 1 ∑ (q) (q) d =t (B − Bdm )2 , d(0) = 0 (9) M m=1 (N +1)m
3. Pan-sharpening algorithm
E=
(7)
k=1
The difference band Bd is appended to the original MS image as the (N + 1)th band. The appended MS is denoted as MS+. It should noted that negative pixel value is allowed in Bd . Compared with MS, MS+ has higher correlation with Pan. The pan-sharpening will be performed on MS+ and original Pan.
x(i+1) = x(i) − λ∇f (x(i) ).
∂E | (n) , ∂Bik Bk =Bk
where step size λ is a small positive number. 4. If the Inequality (8) is satisfied for each band of (q) M S+h , the convergence of SDM is determined; else step 3 is executed again.
3. The difference band Bd is solved as Equation (3): Bd = Y − XA.
(n)
= Bik − λ
(6)
i=1
4. Experimental results and discussions
where K is the number of pixels in Pan image, k is the index number of pixel. Pixel value of expanded MS+ is updated with the gradient of E repeatedly until E has been minimized. In the adaptive model, the difference band Bd plays a role of constraint for pan-sharpening to
The proposed method is evaluated by performing pan-sharpening on dataset acquired by IKONOS, QuickBird, and Landsat-7 ETM+. The dataset contains 3 Pan-MS pairs and each pair is coregistered. All
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(a) IKONOS scene, Sichuan, China (Pan, (b) QuickBird scene, Kolkata, India (Pan, (c) Landsat-7 ETM+ scene, Beijing, China 1000 × 1000, 1m; MS, 250 × 250, 4m, 4 1000 × 1000, 0.6m; MS, 250 × 250, 2.4m, (Pan, 1000 × 1000, 15m; MS, 500 × 500, bands). 4 bands). 30m, 6 bands).
Figure 1. Illustration of false color images of dataset these images have different characteristics in term of Table 1. Results of IKONOS data land cover features and spectral bands, as shown in FigMethod ERGAS Q4 SID SAM ure 1. The well known global quality indexes RelaALM-SDM 1.107 0.985 1.481 27.296 tive Average Spectral Error (ERGAS) [11], and univerSDM 1.926 0.979 2.477 37.351 sal image quality index (Q4 and Qavg) [1] are calcuPCA 2.973 0.765 15.968 97.681 lated to measure the results by comparing the degraded FIHS 2.618 0.950 1.950 33.396 synthetic MS image with the original image. Spectral GS 2.474 0.948 4.299 48.808 Angle Mapper (SAM) [12] and Spectral Information P+XS 1.870 0.959 3.736 45.982 Divergence (SID) [3] are presented to show the spectral distortion in pan-sharpening result. Under the ideal Table 2. Results of QuickBird data condition, ERGAS, SAM, SID should be zero, Q4 and Method ERGAS Q4 SID SAM Qavg should be one. ALM-SDM 0.784 0.990 0.684 19.138 PCA 2.732 0.815 21.286 365.80 Experiment 1: To illustrate the adaptive linear FIHS 1.458 0.963 1.018 24.485 model, we compare our method with [4] on IKONOS GS 1.549 0.962 1.878 32.642 data. In [4], a 4-weights linear model and SDM were P+XS 1.573 0.963 2.216 37.607 used to fuse IKONOS Pan and MS. The proposed method and Kudoh’s method are separately denoted as the best results, and the performance of FIHS is better ALM-SDM and SDM. In experiments, the similar pathan others. That is mainly because the ALM-SDM and rameters of two methods, λ and ε1 are set as the same FIHS consider the difference information between Pan value, λ = 0.5, ε1 = 1000. Experimental results and the linear combination of MS bands. GS and P+XS are shown in the top two rows of Table 1. The redepend on the input data. The performance of them sults of ALM-SDM is better than SDM. Especially for is not stable. The advantage of ALM-SDM is primarERGAS and SAM, our method causes significant deily presented in keeping the spectral consistency, which crease. It can be inferred that the adaptive linear model provides much lower values of SID and SAM. Figure is helpful for preserving spectral information during 2 shows the comparison of the subset of expanded MS pan-sharpening procedure. and the pan-sharpening results using different methods. All these data are normalized and stretched with the same method and parameters. Standard PCA can not give the result with satisfied geometrical quality. There is obvious spectral distortion in the results of FIHS and P+XS. As visual assessment, GS and ALM-SDM provide better results. Comparing the results of GS and ALM-SDM, there is marked spectral distortion of the trees in Figure 2.d, especially on the edge of trees at the top-right corner. All these experimental results indicate that the adaptive linear model reflects the exact relation between Pan
Experiment 2: ALM-SDM is compared with existing techniques. These techniques include standard PCA, fast IHS (FIHS) [10], Gram-Schmidt (GS) method [5] and P+XS method [2]. In all these experiments, the parameters of ALM-SDM, λ, ε1 and ε2 are set as the same values, λ = 0.5, ε1 = 1000, ε2 = 1. Table 1-3 present the quality assessments of pan-sharpening results of different remote sensing data. In Table 3, the data of FIHS method are for the pan-sharpening results of the former 4 bands of Landsat-7 ETM+ data, because of its limitation to the number of bands. ALM-SDM provides
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Table 3. Results of Landsat-7 ETM+ data Method ERGAS Qavg SAM SID ALM-SDM 0.940 0.978 0.233 12.457 PCA 4.915 0.751 3.204 38.939 FIHS∗ 1.643 0.927 0.257 13.030 GS 3.068 0.924 1.394 27.969 P+XS 2.285 0.935 0.957 25.133 and MS images and the proposed iterative fusion algorithm maintains the relation. Compared with other fusion methods mentioned above, our method performs stable on different data and provides the results with better spatial and spectral quality.
(a) Expanded MS.
(b) PCA.
(c) IHS.
(d) Gram-Schmidt.
(e) P+XS.
(f) Proposed Method.
QuickBird, and Landsat-7 ETM+ data. Compared with PCA, FIHS, Gram-Schmidt method, and P+XS, the proposed method provides better pan-sharpening results.
Acknowledgements The QuickBird and Landsat 7 ETM+ data were obtained from Global Land Cover Facility. This work is supported by NSFC (No. 60772156, 60873158), High Tech. 863 (No. 2008AA12Z111), 973 Program (No. 2010CB327902) and the Fundamental Research for the Central Universities.
References [1] L. Alparone, S. Baronti, A. Garzelli, and F. Nencini. A global quality measurement of pan-sharpened multispectral imagery. IEEE Geos. Remote Sensi. Lette., 1(4):313–317, October 2004. [2] C. Ballester, V. Caselles, L. Igual, and J. Verdera. A variational model for p+xs image fusion. Inte. Jour. Comp. Vision, 69(1):43–58, April 2006. [3] C. Chang. Spectral information divergence for hyperspectral image analysis. In Geos. Remote Sensi. Symp., volume 1, pages 509–511, June 1999. [4] J. Kudoh, K. A. Kalpoma, and Y. Kurita. An ikonos image fusion using steepest descent method. In Geos. Remote Sensi. Symp., pages 3231–3234, 2006. [5] C. Laben, V. Bernard, and W. Brower. Process for enhancing the spatial resolution of multispectral imagery using pan-sharpening. US Patent 6.011.875, 2000. [6] T. Ranchin and L. Wald. Fusion of satellite images of different spatial resolutions: assessing the quality of resulting images. Photo. Engin. & Remote Sensi., 63(6):691–699, June 1997. [7] T. Ranchina, B. Aiazzib, L. Alparonec, S. Barontib, and L. Wald. Image fusion-the arsis concept and some successful implementation schemes. ISPRS Jour. Photo. Remote Sensi., 58(1-2):4–18, 2003. [8] G. A. Shaw and H. K. Burke. Spectral imaging for remote sensing. Linc. Labo. Jour., 14(1):3–28, 2003. [9] C. Thomas, T. Ranchin, L. Wald, and J. Chanussot. Synthesis of multispectral images to high spatial resolution: A critical review of fusion methods based on remote sensing physics. IEEE Trans. Geos. Remote Sensi., 46(5):1301–1312, May 2008. [10] T. Tu, P. Huang, C. Hung, and C. Chang. A fast intensity-hue-saturation fusion technique with spectral adjustment for ikonos imagery. IEEE Geos. Remote Sensi. Lette., 1(4):309–312, October 2004. [11] L. Wald. Data Fusion: Definitions and ArchitecturesFusion of Images of Different Spatial Resolutions. Les Presses, Ecole des Mines de Paris, Paris, France, 2002. [12] R. H. Yuhas, A. F. H. Goetz, and J. W. Boardman. Discrimination among semi-arid landscape endmembers using the spectral angle mapper (sam) algorithm. In Summ. 3rd Annu. JPL Airb. Geos. Work., volume 1, pages 147–149, 1992.
Figure 2. A subset of pan-sharpening results for QuickBird data
5. Conclusions In this paper, we propose a new pan-sharpening method based on the adaptive linear model and steepest descent method. The adaptive linear model enhances the correlation between Pan and MS. The iterative pansharpening algorithm effectively utilizes the difference band to preserve the spectral information. The performance of the proposed method is tested on IKONOS, 4515 4523 4495
Pan-Sharpening Using an Adaptive Linear Model Lining Liu1 , Yiding Wang2 , Yunhong Wang1 , Haiyan Yu1 1. School of Computer Science and Engineering, Beihang University, Beijing, China 2. College of Information Engineering, North China University of Technology, Beijing, China lining [email protected], [email protected] [email protected], [email protected]
Abstract In this paper, we propose an algorithm to synthesize high-resolution multispectral images by fusing panchromatic (Pan) images and multispectral (MS) images. The algorithm is based on an adaptive linear model, which is automatically estimated by least square fitting. In this model, a virtual difference band is appended to the MS to guarantee the correlation between the Pan and MS. Then, an iterative procedure is carried out to generate the fused images using steepest descent method. The efficiency of the presented technique is tested by performing pan-sharpening of IKONOS, QuickBird, and Landsat-7 ETM+ datasets. Experimental results show that our method provides better fusion results than other methods.
1. Introduction Due to the inverse relationship between the spectral and spatial resolutions in sensor design [8], most spaceborne optical sensors, such as Landsat, SPOT, IKONOS and QuickBird, provide two different kinds of data, high spectral resolution images at low spatial resolution and high spatial resolution images at low spectral resolution. Many works have demonstrated the benefits of fusing the multispectral (MS) images and panchromatic (Pan) images in land mapping applications [6]. The fusion technique, known as pan-sharpening, has been an active area in the last decade, and many pansharpening methods have been developed [9]. Existing pan-sharpening methods can be categorized into two groups. One is based on the linear correlation between Pan and MS, such as principal component analysis (PCA) based methods, intensity hue saturation (IHS) transform based methods [10], Brovey transform method, and P+XS method [2]. This kind of methods can produce good visual results in most cases, but spec1051-4651/10 $26.00 © 2010 IEEE DOI 10.1109/ICPR.2010.1096
tral distortion is unavoidable for its dependence on the linear relation between Pan and MS. In fact, this relation is certainly not linear. The other is based on multiresolution or multiscale analysis algorithms like wavelet based methods, Gram-Schmidt method [5], and ARSIS (Amlioration de la Rsolution Spatiale par Injection de Structures) concept methods [7]. Results with better spectral quality can be provided by multiscale-based methods, but it has been demonstrated by several experiments that these methods may cause local heterogeneity and degrade the quality of the result [9]. In this paper, we propose a pan-sharpening method based on an adaptive linear model, in which a virtual difference band is appended to the original MS to generate the linear relation between Pan and appended MS. The synthetic high-resolution multispectral image is generated by an iterative algorithm based on steepest descent method (SDM). Compared with existing techniques, the spectral distortion is decreased significantly and the good geometrical quality is achieved.
2. The adaptive linear model For the first kind of pan-sharpening methods introduced in Section 1, it is assumed that Pan equals the linear combination of bands in MS. But the unfitness between real data and the model causes the spectral distortion in pan-sharpening. If we introduce the difference between Pan and the linear combination of MS bands, the relation between Pan and MS would be modeled well. In our fusion framework, the model is presented as Equation (1): P = α0 +
N ∑
αi Bi + Bd ,
(1)
i=1
where P is Pan, αi is the weight of the ith band Bi of MS, and α0 is the constant part of the difference. Bd is the variant part. The difference items ensure that the 4492 4520 4512
preserve the spectral information. So the convergence of the algorithm is determined not only by minimizing E but also by preserving Bd . The whole pan-sharpening algorithm is an iterative optimizing procedure, described as follows: 1. Coefficient matrix A, difference band Bd and MS+ are calculated as the algorithm designed in Section 2. 2. MS+ is expanded to the same size of Pan, and the expanded MS+ is treated as the initial value of the (0) synthetic high-resolution multispectral image M S+h . (q) 3. The pixel value of each band in M S+h is updated as follows:
Equation (1) is tenable, if the relation between Pan and MS is not linear. Whether the Pan-MS pair is in high or low resolution, this model should the same. For the original MS, Bd can be derived as follows: 1. P is resampled to the size of MS to obtain lowresolution Pan Pl ; 2. Coefficient matrix A = [α0 , α1 , · · · , αN ]T is solved using least square fitting method. Define matrixes Y, and X: [ ]T Y = Pl1 Pl2 · · · Plm · · · PlM , 1 B11 · · · Bi1 · · · BN 1 .. .. .. .. . . . . Bim BN m X = 1 B1m . .. .. .. .. . . . 1 B1M · · · · · · · · · BN M where M denotes the number of pixel in MS, m is the index number of pixel in MS and Pan. A = (X T X)−1 X T Y.
(n+1)
Bik
(2)
K ∑ ∂E ∂Bik |Bk =Bk(n) < ε1 ,
(3)
If d(q) − d(q−1) < ε2 , ε2 is a small positive number, the convergence of our algorithm is reached; else the (q) N + 1th band of M S+h is substituted by expanded (q+1) Bd to get M S+h , and return to step 3. 6. The synthetic high-resolution MS is generated by (q) extracting the former N bands from M S+h . It should be noted that the bilinear interpolation is adapted in all resampling processing. The selection of parameters λ, ε1 , ε2 effects the number of iteration and the result’s quality. It’s necessary to set appropriate values to them. λε1 /K should be less than 0.1. ε2 is suggested to be less than 2.
The steepest descent method is a first-order optimization algorithm, which can be represented as Equation (4),(5). minf (x), x ∈ Rn , (4) (5)
SDM has been adopted for pan-sharpening in [2][4]. In our pan-sharpening algorithm, the object function is defined as Equation (6): K ∑ k=1
(α0 +
N ∑
αi Bik + Bdk − Pk )2 ,
(8)
where minimum energy change ε1 is a small positive number. 5. The root mean square error (RMSE) between the (q) degraded N +1th band of M S+h and Bd is calculated as: v u M u 1 ∑ (q) (q) d =t (B − Bdm )2 , d(0) = 0 (9) M m=1 (N +1)m
3. Pan-sharpening algorithm
E=
(7)
k=1
The difference band Bd is appended to the original MS image as the (N + 1)th band. The appended MS is denoted as MS+. It should noted that negative pixel value is allowed in Bd . Compared with MS, MS+ has higher correlation with Pan. The pan-sharpening will be performed on MS+ and original Pan.
x(i+1) = x(i) − λ∇f (x(i) ).
∂E | (n) , ∂Bik Bk =Bk
where step size λ is a small positive number. 4. If the Inequality (8) is satisfied for each band of (q) M S+h , the convergence of SDM is determined; else step 3 is executed again.
3. The difference band Bd is solved as Equation (3): Bd = Y − XA.
(n)
= Bik − λ
(6)
i=1
4. Experimental results and discussions
where K is the number of pixels in Pan image, k is the index number of pixel. Pixel value of expanded MS+ is updated with the gradient of E repeatedly until E has been minimized. In the adaptive model, the difference band Bd plays a role of constraint for pan-sharpening to
The proposed method is evaluated by performing pan-sharpening on dataset acquired by IKONOS, QuickBird, and Landsat-7 ETM+. The dataset contains 3 Pan-MS pairs and each pair is coregistered. All
4513 4521 4493
(a) IKONOS scene, Sichuan, China (Pan, (b) QuickBird scene, Kolkata, India (Pan, (c) Landsat-7 ETM+ scene, Beijing, China 1000 × 1000, 1m; MS, 250 × 250, 4m, 4 1000 × 1000, 0.6m; MS, 250 × 250, 2.4m, (Pan, 1000 × 1000, 15m; MS, 500 × 500, bands). 4 bands). 30m, 6 bands).
Figure 1. Illustration of false color images of dataset these images have different characteristics in term of Table 1. Results of IKONOS data land cover features and spectral bands, as shown in FigMethod ERGAS Q4 SID SAM ure 1. The well known global quality indexes RelaALM-SDM 1.107 0.985 1.481 27.296 tive Average Spectral Error (ERGAS) [11], and univerSDM 1.926 0.979 2.477 37.351 sal image quality index (Q4 and Qavg) [1] are calcuPCA 2.973 0.765 15.968 97.681 lated to measure the results by comparing the degraded FIHS 2.618 0.950 1.950 33.396 synthetic MS image with the original image. Spectral GS 2.474 0.948 4.299 48.808 Angle Mapper (SAM) [12] and Spectral Information P+XS 1.870 0.959 3.736 45.982 Divergence (SID) [3] are presented to show the spectral distortion in pan-sharpening result. Under the ideal Table 2. Results of QuickBird data condition, ERGAS, SAM, SID should be zero, Q4 and Method ERGAS Q4 SID SAM Qavg should be one. ALM-SDM 0.784 0.990 0.684 19.138 PCA 2.732 0.815 21.286 365.80 Experiment 1: To illustrate the adaptive linear FIHS 1.458 0.963 1.018 24.485 model, we compare our method with [4] on IKONOS GS 1.549 0.962 1.878 32.642 data. In [4], a 4-weights linear model and SDM were P+XS 1.573 0.963 2.216 37.607 used to fuse IKONOS Pan and MS. The proposed method and Kudoh’s method are separately denoted as the best results, and the performance of FIHS is better ALM-SDM and SDM. In experiments, the similar pathan others. That is mainly because the ALM-SDM and rameters of two methods, λ and ε1 are set as the same FIHS consider the difference information between Pan value, λ = 0.5, ε1 = 1000. Experimental results and the linear combination of MS bands. GS and P+XS are shown in the top two rows of Table 1. The redepend on the input data. The performance of them sults of ALM-SDM is better than SDM. Especially for is not stable. The advantage of ALM-SDM is primarERGAS and SAM, our method causes significant deily presented in keeping the spectral consistency, which crease. It can be inferred that the adaptive linear model provides much lower values of SID and SAM. Figure is helpful for preserving spectral information during 2 shows the comparison of the subset of expanded MS pan-sharpening procedure. and the pan-sharpening results using different methods. All these data are normalized and stretched with the same method and parameters. Standard PCA can not give the result with satisfied geometrical quality. There is obvious spectral distortion in the results of FIHS and P+XS. As visual assessment, GS and ALM-SDM provide better results. Comparing the results of GS and ALM-SDM, there is marked spectral distortion of the trees in Figure 2.d, especially on the edge of trees at the top-right corner. All these experimental results indicate that the adaptive linear model reflects the exact relation between Pan
Experiment 2: ALM-SDM is compared with existing techniques. These techniques include standard PCA, fast IHS (FIHS) [10], Gram-Schmidt (GS) method [5] and P+XS method [2]. In all these experiments, the parameters of ALM-SDM, λ, ε1 and ε2 are set as the same values, λ = 0.5, ε1 = 1000, ε2 = 1. Table 1-3 present the quality assessments of pan-sharpening results of different remote sensing data. In Table 3, the data of FIHS method are for the pan-sharpening results of the former 4 bands of Landsat-7 ETM+ data, because of its limitation to the number of bands. ALM-SDM provides
4514 4522 4494
Table 3. Results of Landsat-7 ETM+ data Method ERGAS Qavg SAM SID ALM-SDM 0.940 0.978 0.233 12.457 PCA 4.915 0.751 3.204 38.939 FIHS∗ 1.643 0.927 0.257 13.030 GS 3.068 0.924 1.394 27.969 P+XS 2.285 0.935 0.957 25.133 and MS images and the proposed iterative fusion algorithm maintains the relation. Compared with other fusion methods mentioned above, our method performs stable on different data and provides the results with better spatial and spectral quality.
(a) Expanded MS.
(b) PCA.
(c) IHS.
(d) Gram-Schmidt.
(e) P+XS.
(f) Proposed Method.
QuickBird, and Landsat-7 ETM+ data. Compared with PCA, FIHS, Gram-Schmidt method, and P+XS, the proposed method provides better pan-sharpening results.
Acknowledgements The QuickBird and Landsat 7 ETM+ data were obtained from Global Land Cover Facility. This work is supported by NSFC (No. 60772156, 60873158), High Tech. 863 (No. 2008AA12Z111), 973 Program (No. 2010CB327902) and the Fundamental Research for the Central Universities.
References [1] L. Alparone, S. Baronti, A. Garzelli, and F. Nencini. A global quality measurement of pan-sharpened multispectral imagery. IEEE Geos. Remote Sensi. Lette., 1(4):313–317, October 2004. [2] C. Ballester, V. Caselles, L. Igual, and J. Verdera. A variational model for p+xs image fusion. Inte. Jour. Comp. Vision, 69(1):43–58, April 2006. [3] C. Chang. Spectral information divergence for hyperspectral image analysis. In Geos. Remote Sensi. Symp., volume 1, pages 509–511, June 1999. [4] J. Kudoh, K. A. Kalpoma, and Y. Kurita. An ikonos image fusion using steepest descent method. In Geos. Remote Sensi. Symp., pages 3231–3234, 2006. [5] C. Laben, V. Bernard, and W. Brower. Process for enhancing the spatial resolution of multispectral imagery using pan-sharpening. US Patent 6.011.875, 2000. [6] T. Ranchin and L. Wald. Fusion of satellite images of different spatial resolutions: assessing the quality of resulting images. Photo. Engin. & Remote Sensi., 63(6):691–699, June 1997. [7] T. Ranchina, B. Aiazzib, L. Alparonec, S. Barontib, and L. Wald. Image fusion-the arsis concept and some successful implementation schemes. ISPRS Jour. Photo. Remote Sensi., 58(1-2):4–18, 2003. [8] G. A. Shaw and H. K. Burke. Spectral imaging for remote sensing. Linc. Labo. Jour., 14(1):3–28, 2003. [9] C. Thomas, T. Ranchin, L. Wald, and J. Chanussot. Synthesis of multispectral images to high spatial resolution: A critical review of fusion methods based on remote sensing physics. IEEE Trans. Geos. Remote Sensi., 46(5):1301–1312, May 2008. [10] T. Tu, P. Huang, C. Hung, and C. Chang. A fast intensity-hue-saturation fusion technique with spectral adjustment for ikonos imagery. IEEE Geos. Remote Sensi. Lette., 1(4):309–312, October 2004. [11] L. Wald. Data Fusion: Definitions and ArchitecturesFusion of Images of Different Spatial Resolutions. Les Presses, Ecole des Mines de Paris, Paris, France, 2002. [12] R. H. Yuhas, A. F. H. Goetz, and J. W. Boardman. Discrimination among semi-arid landscape endmembers using the spectral angle mapper (sam) algorithm. In Summ. 3rd Annu. JPL Airb. Geos. Work., volume 1, pages 147–149, 1992.
Figure 2. A subset of pan-sharpening results for QuickBird data
5. Conclusions In this paper, we propose a new pan-sharpening method based on the adaptive linear model and steepest descent method. The adaptive linear model enhances the correlation between Pan and MS. The iterative pansharpening algorithm effectively utilizes the difference band to preserve the spectral information. The performance of the proposed method is tested on IKONOS, 4515 4523 4495
