Adaptive regularized scheme for remote sensing image fusion

Abstract

We propose an adaptive regularized algorithm for remote sensing image fusion based on variational methods. In the algorithm, we integrate the inputs using a “grey world” assumption to achieve visual uniformity. We propose a fusion operator that can automatically select the total variation (TV)–L₁ term for edges and L₂-terms for non-edges. To implement our algorithm, we use the steepest descent method to solve the corresponding Euler–Lagrange equation. Experimental results show that the proposed algorithm achieves remarkable results.

Key words： remote sensing image fusion; adaptive regulariser; variational method; steepest descent method

Acknowledgements

This work was supported by the National Basic Research Program of China (No. 2011CB707104) and the National Natural Science Foundation of China (Grant No. 61273298).

Supplementary material is available in the online version of this article at http://dx.doi.org/10.1007/s11707-015-0514-7 and is accessible for authorized users.

References

1 Agrawal D, Singhai J (2010). Multi-focus image fusion using modified pulse coupled neural network for improved image quality. IET Image Processing, 4(6): 443–451

2 Aubert G, Kornprobst P (2009). Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations. Applied Mathematical Sciences. Berlin: Springer-Verlag

3 Bertalmio M, Caselles V, Provenzi E, Rizzi A (2007). Perceptual color correction through variational techniques. IEEE Trans Image Process, 16(4): 1058–1072

4 Brelstaff G J, Párraga A, Troscianko T, Carr D (1995). Hyper spectral camera system: acquisition and analysis. In: Satellite Remote Sensing II. International Society for Optics and Photonics: 150–159

5 Buchsbaum G (1980). A spatial processor model for object color perception. J Franklin Inst, 310(1): 1–26

6 Chai Y, Li H, Zhang X (2012). Multi-focus image fusion based on features contrast of multi-scale products in non-subsampled contourlet transform domain. Optik-International Journal for Light and Electron Optics, 123(7): 569–581

7 Chan T F, Esedoglu S (2005). Aspects of total variation regularized l1function approximation. SIAM J Appl Math, 65(5): 1817–1837

8 Chan T, Shen J, Vese L (2003). Variational PDE models in image processing. Not Am Math Soc, 50(1): 14–26

9 Cvejic N, Seppanen T, Godsill S (2009). A no reference image fusion metric based on the regional importance measure. IEEE Journal Of Selected Topics In Signal Processing, 3(2): 212–221

10 Ellmauthaler A, Pagliari C L, Da Silva E A (2013). Multi-scale image fusion using the undecimated wavelet transform with spectral factorization and nonorthogonal filter banks. IEEE Trans Image Process, 22(3): 1005–1017

11 El-taweel G S, Helmy A K (2013). Image fusion scheme based on modified dual pulse coupled neural network. IET Image Processing, 7(5): 407–414

12 Fang F, Li F, Zhang G, Shen C (2013). A variational method for multisource remote-sensing image fusion. Int J Remote Sens, 34(7): 2470–2486

13 Gao G R, Lu P X, Feng D Z (2013). Multi-focus image fusion based on non-sub-sampled shear-let transform. IET Image Processing, 7(6): 633–639

15 Hinterberger W, Scherzer O (2006). Variational methods on the space of functions of bounded hessian for convexification and de-noising. Computing, 76(1–2): 109–133

16 James A, Dasarathy B (2014). Medical image fusion: a survey of the state of the art. Inf Fusion, 19: 4–19

17 Kim Y, Lee C, Han D, Kim Y, Kim Y (2011). Improved additive-wavelet image fusion. IEEE Transactions on Geoscience and Remote Sensing Letters, 8(2): 263–267

18 Kluckner S, Pock T, Bischof H (2010). Exploiting redundancy for aerial image fusion using convex optimization. Proceedings of the 32nd DAGM conference on Pattern Recognition, Darmstadt, Germany

19 Kong W, Lei Y, Lei Y, Lu S (2011). Image fusion technique based on non-sub-sampled contour-let transform and adaptive unit-fast-linking pulse-coupled neural network. IET Image Processing, 5(2): 113– 121

20 Kumar M, Dass S (2009). A total variation-based algorithm for pixel-level image fusion. IEEE Trans Image Process, 18(9): 2137–2143

21 Li X, He M, Roux M (2010). Multi-focus image fusion based on redundant wavelet transform. IET Image Processing, 4(4): 283–293

22 Liu G, Shen Y (2012). Ultrasonic image fusion using compressed sensing. Electron Lett, 48(19): 1182–1184

24 Liu X, Zhou Y, Wang J (2014). Image fusion based on shearlet transform and regional features. AEU, Int J Electron Commun, 68(6): 471– 477

25 Lustig M, Donoho D, Pauly J M (2007). Sparse MRI: the application of compressed sensing for rapid MR imaging. Magn Reson Med, 58(6): 1182–1195

26 Lysaker M, Lundervold A, Tai X C (2003). Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time. IEEE Trans Image Process, 12(12): 1579–1590

27 Mahbubur Rahman S M, Omair Ahmad M, Swamy M N S (2010). Contrast-based fusion of noisy images using discrete wavelet transform. IET Image Processing, 4(5): 374–384

29 Nikolova M (2004). A variational approach to remove outliers and impulse noise. J Math Imaging Vis, 20(1–2): 99–120

30 Papafitsoros K, Schönlieb C B (2014). A combined first and second order variational approach for image reconstruction. J Math Imaging Vis, 48(2): 308–338

31 Petrovic V (2004). Subjective image fusion evaluation data. Imaging Science Biomedical Engineering. University of Manchester:1–9

33 Piella G (2009). Image fusion for enhanced visualization: a variational approach. Int J Comput Vis, 83(1): 1–11

35 Pock T, Zebedin L, Bischof H (2011). TGV-fusion. In: Calude C S, Rozenberg A G, Salomaa A, eds. Maurer Festschrift. LNCS, 6570: 245–258

36 Pouteau R, Stoll B, Chabrier S (2010). Multi-source SVM fusion for environmental monitoring in marquesas archipelago. In: Geoscience and Remote Sensing Symposium (IGARSS), 2010 IEEE International, 2719–2722

38 Rudin L I, Osher S, Fatemi E (1992). Non-linear total variation based noise removal algorithms. Physica D, 60(1): 259–268

39 Sapiro G (2001). Geometric Partial Differential Equations and Image Analysis. Cambridge University Press

40 Schowengerdt R A (2006). Remote sensing: Models and Methods for Image Processing (3rd Edition). Academic Press

41 Socolinsky D A (2000). A variational Approach to Image Fusion. Dissertation for PhD degree. The Johns Hopkins University, April 2000

42 Socolinsky D A, Wolff L B (2002). Multispectral image visualization through first-order fusion. IEEE Trans Image Process, 11(8): 923–931

43 Stathaki (2008). Image Fusion: Algorithms and Applications. Amsterdam: Elsevier

44 Tafti P D, Stalder A F, Delgado-Gonzalo R, Unser M (2011). Variational enhancement and de-noising of flow field images. 8th IEEE International symposium on biomedical imaging: from Nano to Macro: 1061–1064

45 Tikhonov A N (1943). On the stability of inverse problems. Dokl Akad Nauk SSSR, 39(5): 195–198

46 Tran M P, Peteri R, Bergounioux M (2012). De-noising 3D medical images using a second order variational model and wavelet shrinkage. In: Image Analysis and Recognition. Berlin: Springer, 138–145

48 Wang C, Ye Z F (2007). Perceptual contrast-based image fusion: a variational approach. Acta Automatica Sinica, 33(2): 132–137

48 Wang L, Li B, Tian L (2014). Multi-modal medical volumetric data fusion using 3D discrete shearlet transform and global-to-local rule. IEEE Trans Biomed Eng, 61(1): 197–206

49 Wang W W, Shui P L, Feng X C (2008). Variational models for fusion and de-noising of multi-focus images. IEEE Signal Process Lett, 15: 65–68

51 Wang Z, Ziou D, Armenakis C, Li D, Li Q (2005). A comparative analysis of image fusion methods. IEEE Trans Geosci Rem Sens, 43(6): 1391–1402

53 Yang B, Li S (2010). Multi-focus image fusion and restoration with sparse representation. IEEE Trans Instrum Meas, 59(4): 884–892

54 Yang L, Guo B, Ni W (2008). Multimodality medical image fusion based on multi-scale geometric analysis of contourlet transform. Neurocomputing, 72(1–3): 203–211

55 Yang Z Z, Yang Z (2013). Novel multi-focus image fusion and reconstruction framework based on compressed sensing. IET Image Processing, 7(9): 837–847

56 Yuan J, Miles B, Shi J, Garvin G, Tai X C and A. Fenster A (2012). Efficient convex optimization approaches to variational image fusion. UCLA Tech. Report CAM-11-86

57 Zhang X, Chan T F (2010). Wavelet inpainting by nonlocal total variation. Inverse Problems and Imaging, 4(1): 191–210

58 Zheng S, Shi W, Liu J, Zhu G, Tian J (2007). Multisource image fusion method using support value transform. IEEE Trans Image Process, 16: 1