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.
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
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
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
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
Geman D., Yang C. (1995) Nonlinear image recovery with half-quadratic regularization. IEEE Transactions on Image Processing 4(7): 932–946
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
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
Lam E.Y. (2003) Noise in superresolution reconstruction. Optics Letters 28(12): 2234–2236
Lee S.H., Cho N.I., Park J.-I. (2003) Directional regularisation for constrained iterative image restoration. Electronics Letters 39(23): 1642–1643
Mico V., Zalevsky Z., García J. (2006) Superresolution optical system by common-path interferometry. Optics Express 14(12): 5168–5177
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
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
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
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
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
Author information
Authors and Affiliations
Corresponding author
Rights 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
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11045-008-0072-1