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.

Keywords

remote sensing image fusion / adaptive regulariser / variational method / steepest descent method

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

[14] 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

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

[16] 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

[17] 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

[18] 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

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

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

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

[22] 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

[23] 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

[24] 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

[25] 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

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

[27] 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

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

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

[30] 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

[31] 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

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

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

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

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

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

[37] Stathaki (2008). Image Fusion: Algorithms and Applications. Amsterdam: Elsevier

[38] 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

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

[40] 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

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

[42] 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

[43] 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

[44] 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

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

[46] 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

[47] 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

[48] 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

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

[50] 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

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag Berlin Heidelberg