Skip to main content
Log in

Superresolution reconstruction using nonlinear gradient-based regularization

  • Published:
Multidimensional Systems and Signal Processing Aims and scope Submit manuscript

Abstract

This paper discusses the problem of superresolution reconstruction. To preserve edges accurately and efficiently in the reconstruction, we propose a nonlinear gradient-based regularization that uses the gradient vector field of a preliminary high resolution image to configure a regularization matrix and compute the regularization parameters. Compared with other existing methods, it not only enhances the spatial resolution of the resulting images, but can also preserve edges and smooth noise to a greater extent. The advantages are shown in simulations and experiments with synthetic and real images.

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.

Institutional subscriptions

Similar content being viewed by others

References

  • Blu, T., Bay, H., & Unser, M. (2002). A new high-resolution processing method for the deconvolution of optical coherence tomography signals. In IEEE International Symposium on Biomedical Imaging, Vol. 3, pp. 777–780.

  • Cao N., Nehorai A., Jacob M. (2007) Image reconstruction for diffuse optical tomography using sparsity regularization and expectation-maximization algorithm. Optics Express 15(21): 13695–13708

    Article  Google Scholar 

  • Chan W.-S., Lam E.Y., Ng M.K., Mak G.Y. (2007) Super-resolution reconstruction in a computational compound-eye imaging system. Multidimensional Systems and Signal Processing 18(2–3): 83–101

    Article  MATH  MathSciNet  Google Scholar 

  • Charbonnier P., Blanc-Féraud L., Aubert G., Barlaud M. (1997) Deterministic edge-preserving regularization in computed imaging. IEEE Transactions on Image Processing 6(2): 298–311

    Article  Google Scholar 

  • Deriche, R., Kornprobst, P., Nikolova, M., & Ng, M. K. (2003). Half-quadratic regularization for MRI image restoration. In Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing, Vol. 6, pp. 585–588.

  • Elad M., Feuer A. (1997) Restoration of single super-resolution image from several blurred, noisy and down-sampled measure images. IEEE Transactions on Image Processing 6(12): 1646–1658

    Article  Google Scholar 

  • Geman D., Yang C. (1995) Nonlinear image recovery with half-quadratic regularization. IEEE Transactions on Image Processing 4(7): 932–946

    Article  Google Scholar 

  • Kennedy J.A., Israel O., Frenkel A., Bar-Shalom R., Azhari H. (2006) Super-resolution in PET imaging. IEEE Transactions on Medical Imaging 25(2): 137–147

    Article  Google Scholar 

  • Kilmer M.E., O’Leary D.P. (2001) Choosing regularization parameters in iterative methods for Ill-posed problems. SIAM Journal on Matrix Analysis and Applications 22(4): 1204–1221

    Article  MATH  MathSciNet  Google Scholar 

  • Lam E.Y. (2003) Noise in superresolution reconstruction. Optics Letters 28(12): 2234–2236

    Article  Google Scholar 

  • Lee S.H., Cho N.I., Park J.-I. (2003) Directional regularisation for constrained iterative image restoration. Electronics Letters 39(23): 1642–1643

    Article  Google Scholar 

  • Mico V., Zalevsky Z., García J. (2006) Superresolution optical system by common-path interferometry. Optics Express 14(12): 5168–5177

    Article  Google Scholar 

  • Ng, M. K., Shen, H., Lam, E., & Zhang, L. (2007). A total variation regularization based super-resolution reconstruction algorithm for digital video. EURASIP Journal on Advances in Signal Processing, 2007, 1–16, Article ID 74585.

  • Nikolova, M., & Ng, M. K. (2001). Fast image reconstruction algorithms combining half-quadratic regularization and preconditioning. In Proceedings of International Conference on Image Processing, Vol. 1, pp. 277–280.

  • Nikolova M., Ng M.K. (2005) Fast image reconstruction algorithms combining half-quadratic regularization and preconditioning. SIAM Journal on Scientific Computing 27: 937–966

    Article  MATH  MathSciNet  Google Scholar 

  • Park S.C., Park M.K., Kang M.G. (2003) Super-resolution image reconstruction: A rechnical overview. IEEE Signal Processing Magazine 20(3): 21–36

    Article  Google Scholar 

  • Peled S., Yeshurun Y. (2001) Superresolution in MRI: Application to human white matter fiber tract visualization by diffusion tensor imaging. Magnetic Resonance Imaging 45(1): 29–35

    Google Scholar 

  • Shin, J.-H., Sun, Y., Joung, W.-C., Paik, J.-K., & Abidi, M. A. (2001). Adaptive regularized noise smoothing of dense range image using directional Laplacian operators. In Proceedings of SPIE Three-Dimensional Image Capture and Applications IV, Vol. 4298, pp. 119–126.

  • Vanzella W., Pellegrino F.A., Torre V. (2004) Self-adaptive regularization. IEEE Transactions on Pattern Analysis and Machine Intelligence 26(6): 804–809

    Article  Google Scholar 

  • Wang, Y., Hu, J., & Schroder, H. (2005). A gradient based weighted averaging method for estimation of fingerprint orientation fields. In Proceedings of Digital Image Computing: Techniques and Applications, p. 29.

  • Watzenig D., Brandstätter B., Holler G. (2004) Adaptive regularization parameter adjustment for reconstruction problems. IEEE Transactions on Magnetics 40(2): 1116–1119

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xin Zhang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, X., Lam, E.Y. Superresolution reconstruction using nonlinear gradient-based regularization. Multidim Syst Sign Process 20, 375–384 (2009). https://doi.org/10.1007/s11045-008-0072-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11045-008-0072-1

Keywords

Navigation