Skip to main content
Log in

Abstract

We present a novel image fusion scheme based on gradient and scrambled block Hadamard ensemble (SBHE) sampling for compressive sensing imaging. First, source images are compressed by compressive sensing, to facilitate the transmission of the sensor. In the fusion phase, the image gradient is calculated to reflect the abundance of its contour information. By compositing the gradient of each image, gradient-based weights are obtained, with which compressive sensing coefficients are achieved. Finally, inverse transformation is applied to the coefficients derived from fusion, and the fused image is obtained. Information entropy (IE), Xydeas’s and Piella’s metrics are applied as non-reference objective metrics to evaluate the fusion quality in line with different fusion schemes. In addition, different image fusion application scenarios are applied to explore the scenario adaptability of the proposed scheme. Simulation results demonstrate that the gradient-based scheme has the best performance, in terms of both subjective judgment and objective metrics. Furthermore, the gradient-based fusion scheme proposed in this paper can be applied in different fusion scenarios.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Amolins, K., Zhang, Y., Dare, P., 2007. Wavelet based image fusion techniques—an introduction, review and comparison. ISPRS J. Photogram. Remote Sens., 62(4): 249–263. [doi:10.1016/j.isprsjprs.2007.05.009]

    Article  Google Scholar 

  • Byeungwoo, J., Landgrebe, D.A., 1999. Decision fusion approach for multitemporal classification. IEEE Trans. Geosci. Remote Sens., 37(3):1227–1233. [doi:10.1109/36.763278]

    Article  Google Scholar 

  • Candès, E.J., Romberg, J., 2005. l 1-Magic: Recovery of Sparse Signals via Convex Programming. Available from http://www.acm.caltech.edu/l1magic/

    Google Scholar 

  • Candès, E.J., Tao, T., 2006. Near-optimal signal recovery from random projections: universal encoding strategies. IEEE Trans. Inform. Theory, 52(12):5406–5425. [doi:10.1109/TIT.2006.885507]

    Article  MATH  MathSciNet  Google Scholar 

  • Candès, E.J., Wakin, M.B., 2008. An introduction to compressive sampling. IEEE Signal Process. Mag., 25(2):21–30. [doi:10.1109/MSP.2007.914731]

    Article  Google Scholar 

  • Chen, R.Y., Li, S., Yang, R., et al., 2008. Multi-focus images fusion based on data assimilation and genetic algorithm. Proc. Int. Conf. on Computer Science and Software Engineering, p.249–252. [doi:10.1109/CSSE.2008.525]

    Google Scholar 

  • Chen, S.S., Donoho, D.L., Saunders, M.A., 1998. Atomic decomposition by basis pursuit. SIAM J. Sci. Comput., 20(1):33–61. [doi:10.1137/S1064827596304010]

    Article  MathSciNet  Google Scholar 

  • Ding, M., Wei, L., Wang, B.F., 2013. Research on fusion method for infrared and visible images via compressive sensing. Infrared Phys. Technol., 57:56–67. [doi:10.1016/j.infrared.2012.12.014]

    Article  Google Scholar 

  • Do, T.T., Lu, G., Nguyen, N.H., et al., 2012. Fast and efficient compressive sensing using structurally random matrices. IEEE Trans. Signal Process., 60(1):139–154. [doi:10.1109/TSP.2011.2170977]

    Article  MathSciNet  Google Scholar 

  • Donoho, D.L., 2006. Compressed sensing. IEEE Trans. Inform. Theory, 52(4):1289–1306. [doi:10.1109/TIT.2006.871582]

    Article  MATH  MathSciNet  Google Scholar 

  • Duarte, M.F., Davenpot, M.A., Takhar, D., et al., 2008. Single-pixel imaging via compressive sampling. IEEE Signal Process. Mag., 25(2):83–91. [doi:10.1109/MSP.2007.914730]

    Article  Google Scholar 

  • Figueiredo, M.A.T., Nowak, R.D., Wright, S.J., 2007. Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems. IEEE J. Sel. Topics Signal Process., 1(4):586–597. [doi:10.1109/JSTSP.2007.910281]

    Article  Google Scholar 

  • Han, J.J., Loffeld, O., Hartmann, K., et al., 2010. Multi image fusion based on compressive sensing. Proc. Int. Conf. on Audio Language and Image Processing, p.1463–1469. [doi:10.1109/ICALIP.2010.5684502]

    Google Scholar 

  • Jolliffe, I.T., 1986. Principal Component Analysis. Springer.

    Book  Google Scholar 

  • Kang, B., Zhu, W.P., Yan, J., 2013. Fusion framework for multi-focus images based on compressed sensing. IET Image Process., 7(4):290–299. [doi:10.1049/iet-ipr.2012.0543]

    Article  MathSciNet  Google Scholar 

  • Li, S.T., Yang, B., 2008. Multifocus image fusion by combining curvelet and wavelet transform. Patt. Recog. Lett., 29(9):1295–1301. [doi:10.1016/j.patrec.2008.02.002]

    Article  Google Scholar 

  • Li, S.T., Kwok, J.T.Y., Tsang, I.W., et al., 2004. Fusing images with different focuses using support vector machines. IEEE Trans. Neur. Netw., 15(6):1555–1561. [doi:10.1109/TNN.2004.837780]

    Article  Google Scholar 

  • Li, X., Qin, S.Y., 2011. Efficient fusion for infrared and visible images based on compressive sensing principle. IET Image Process., 5(2):141–147. [doi:10.1049/iet-ipr.2010.0084]

    Article  Google Scholar 

  • Liu, Z., Tsukada, K., Hanasaki, K., et al., 2001. Image fusion by using steerable pyramid. Patt. Recog. Lett., 22(9): 929–939. [doi:10.1016/S0167-8655(01)00047-2]

    Article  MATH  Google Scholar 

  • Luo, X.Y., Zhang, J., Yang, J.Y., et al., 2009. Image fusion in compressed sensing. Proc. 16th IEEE Int. Conf. on Image Processing, p.2205–2208. [doi:10.1109/ICIP.2009.5413866]

    Google Scholar 

  • Pajares, G., de la Cruz, J.M., 2004. A wavelet-based image fusion tutorial. Patt. Recog., 37(9):1855–1872. [doi:10.1016/j.patcog.2004.03.010]

    Article  Google Scholar 

  • Petrović, V.S., Xydeas, C.S., 2004. Gradient-based multiresolution image fusion. IEEE Trans. Image Process., 13(2):228–237. [doi:10.1109/TIP.2004.823821]

    Article  Google Scholar 

  • Piella, G., Heijmans, H., 2003. A new quality metric for image fusion. Proc. Int. Conf. on Image Processing, p.173–176. [doi:10.1109/ICIP.2003.1247209]

    Google Scholar 

  • Qu, G.H., Zhang, D.L., Yan, P.F., 2002. Information measure for performance of image fusion. Electron. Lett., 38(7):313–315. [doi:10.1049/el:20020212]

    Article  Google Scholar 

  • Romberg, J., 2008. Imaging via compressive sampling. IEEE Signal Process. Mag., 25(2):14–20. [doi:10.1109/MSP.2007.914729]

    Article  Google Scholar 

  • Ross, A.A., Govindarajan, R., 2005. Feature level fusion of hand and face biometrics. Proc. SPIE, p.196–204. [doi:10.1117/12.606093]

    Google Scholar 

  • Shi, W.Z., Zhu, C.Q., Tian, Y., et al., 2005. Wavelet-based image fusion and quality assessment. Int. J. Appl. Earth Observ. Geoinform., 6(3–4):241–251. [doi:10.1016/j.jag.2004.10.010]

    Article  Google Scholar 

  • Smith, L.I., 2002. A Tutorial on Principal Components Analysis. Available from www.cs.otago.ac.nz/cosc453/student_tutorials/principal_components.pdf.

    Google Scholar 

  • Tropp, J., Gilbert, A.C., 2007. Signal recovery from random measurements via orthogonal matching pursuit. IEEE Trans. Inform. Theory, 53(12):4655–4666. [doi:10.1109/TIT.2007.909108]

    Article  MATH  MathSciNet  Google Scholar 

  • Wan, T., Qin, Z.C., 2011. An application of compressive sensing for image fusion. Int. J. Comput. Math., 88(18): 3–9. [doi:10.1080/00207160.2011.598229]

    Article  Google Scholar 

  • Wang, R., Du, L.F., 2014. Infrared and visible image fusion based on random projection and sparse representation. Int. J. Remote Sens., 35(5):1640–1652. [doi:10.1080/01431161.2014.880819]

    Article  Google Scholar 

  • Wang, Y., Yang, J.F., Yin, W., et al., 2008. A new alternating minimization algorithm for total variation image reconstruction. SIAM J. Image Sci., 1(3):248–272. [doi:10.1137/080724265]

    Article  MATH  MathSciNet  Google Scholar 

  • Xydeas, C.S., Petrović, V., 2000. Objective image fusion performance measure. Electron. Lett., 36(4):308–309. [doi:10.1049/el:20000267]

    Article  Google Scholar 

  • Yang, X.H., Jin, H.Y., Jiao, L.C., 2007. Adaptive image fusion algorithm for infrared and visible light images based on DT-CWT. J. Infrared Millim. Waves, 26(6):419–424 (in Chinese).

    Google Scholar 

  • Yang, Y., Han, C.Z., Kang, X., et al., 2007. An overview on pixel-level image fusion in remote sensing. Proc. IEEE Int. Conf. on Automation and Logistics, p.2339–2344. [doi:10.1109/ICAL.2007.4338968]

    Google Scholar 

  • Zheng, Y.Z., Qin, Z., 2009. Region-based image fusion method using bidimensional empirical mode decomposition. J. Electron. Imag., 18(1):013008. [doi:10.1117/1.3099703]

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yang Chen.

Additional information

Project supported by the National S&T Major Program (No. 9140A1550212 JW01047) and the ‘Twelfth Five’ Preliminary Research Project of PLA (No. 402040202)

ORCID: Yang CHEN, http://orcid.org/0000-0003-0927-000X

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chen, Y., Qin, Z. Gradient-based compressive image fusion. Frontiers Inf Technol Electronic Eng 16, 227–237 (2015). https://doi.org/10.1631/FITEE.1400217

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1631/FITEE.1400217

Key words

CLC number

Navigation