Abstract
A large number of applications in image processing and computer vision depend on image quality. In this paper, combining the forward diffusion with the backward diffusion by different weights, we present an adaptive bidirectional diffusion method for image denoising and deblurring simultaneously. Further, we introduce a gradient factor into the data fidelity term, which forms a spatially varying constraint and allows a better restoration of image edges and fine details. In order to obtain a stable solution, we develop a numerically stable scheme and give its theoretical analysis. Finally, we show advantages of this method in deblurring edges, denoising and restoring fine details of image compared with other related methods in experiments.
Similar content being viewed by others
References
Zhang Y D, Wu L N. Improved image filter based on SPCNN. Sci China Ser F-Inf Sci, 2008, 51: 2115–2125
Chan T F, Shen J. Image Processing and Analysis: Variational, PDE, Wavelet, and Stochastic Methods. Philadelphia: the Society for Industrial and Applied Mathematics, 2005
Tikhonov A N, Arsenin V Y. Solutions of Ill-posed Problems. Washington DC: Winston & Sons Incorporation, 1977
Nordstrom K N. Biased anisotropic diffusion—a unified regularization and diffusion approach to edge detection. Imag Vision Comput, 1990, 8: 318–327
Witkin A P. Scale-space filtering. In: Proceedings of the International Joint Conference on Artificial Intelligence, Karlsruhe, West Germany, 1983. 1019–1021
Koenderink J J. The structure of images. Bio Cybern, 1984, 50: 363–370
Perona P, Malik J. Scale-space and edge detection using anisotropic diffusion. IEEE Trans Patt Anal Mach Intell, 1990, 12: 629–639
Alvarez L, Lions P L, Morel J M. Image selective smoothing and edge detection by nonlinear diffusion II. SIAM J Num Anal, 1992, 29: 845–866
Kornprobst P, Deriche R, Aubert G. Image coupling, restoration and enhancement via pde’s. In: Proceedings of the IEEE International Conference on Image Processing, Washington, DC, 1997. 458–461
Keeling S L, Stollberger R. Nonlinear anisotropic diffusion filtering for multiscale edge enhancement. Inverse Problems, 2002, 18: 175–190
Gilboa G, Sochen N, Zeevi Y Y. Forward-and-backward diffusion processes for adaptive image enhancement and denoising. IEEE Trans Image Process, 2002, 11: 689–703
Fu S, Ruan Q, Geng Y, et al. Feature-oriented coupled bidirectional flow for image denoising and edge sharpening. In: Proceedings of the IEEE International Region 10 Conference (Tencon 2005), Melbourne, Qld, 2006. 1–5
Aubert G, Kornprobst P. Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations. 2nd ed. New York: Springer-Verlag, 2006
Liu F. Diffusion filtering in image processing based on wavelet transform. Sci China Ser F-Inf Sci, 2006, 49: 494–503
Fu S, Ruan Q, Wang W, et al. A feature-dependent fuzzy bidirectional flow for adaptive image sharpening. Neurocomputing, 2007, 70: 883–895
Fu S, Ruan Q, Mu C, et al. Feature preserving coupled bidirectional flow for edge sharpening and image enhancement. Chin J Comput, 2008, 31: 529–535
Gabor D. Information theory in electron microscopy. Lab Invest, 1965, 14: 801–807
Hummel R A, Kimia B, Zucker SW. Deblurring Gaussian blur. Comput Vision Graph Image Process, 1987, 38: 66–80
Kuijper A. Geometrical pdes based on second-order derivatives of gauge coordinates in image processing. Image Vision Comput, 2009, 27: 1023–1034
Kovasznay L S G, Joseph H M. Image processing. Proc Instit Radio Eng, 1955, 43: 560–570
Wang W W, Wang Z M, Yuan Z Y, et al. A fast and adaptive method for complex-valued sar image denoising based on lk norm regularization. Sci China Ser F-Inf Sci, 2009, 52: 138–148
Yang J Y, Peng Y G, Xu W L, et al. Ways to sparse representation: an overview. Sci China Ser F-Inf Sci, 2009, 52: 695–703
Fu S, Zhang C. Adaptive non-convex total variation regularisation for image restoration. IET Electr Lett, 2010, 46: 907–908
Lindenbaum M, Fischer M, Bruckstein A. On Gabor’s contribution to image enhancement. Patt Recog, 1994, 27: 1–8
Buades A, Coll B, Morel J M. Image enhancement by non-local reverse heat equation. Technical report, Centre de Mathématiques et de Leurs Applications (CMLA), France, 2006
Gilboa G, Sochen N, Zeevi Y Y. Variational denoising of partly textured images by spatially varying constraints. IEEE Trans Image Process, 2006, 15: 2281–2289
Osher S, Paragios N. Geometric Level Set Methods in Imaging, Vision, and Graphics. New York: Springer-Verlag, 2003
Osher S, Fedkiw R P. Level Set Methods and Dynamic Implicit Surfaces. New York: Springer-Verlag, 2002
Weickert J, Romeny B, Viergever M A. Efficient and reliable schemes for nonlinear diffusion filtering. IEEE Trans Image Process, 1998, 7: 398–410
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Fu, S., Zhang, C. Adaptive bidirectional diffusion for image restoration. Sci. China Inf. Sci. 53, 2452–2460 (2010). https://doi.org/10.1007/s11432-010-4108-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11432-010-4108-4