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http://dx.doi.org/10.9717/kmms.2014.17.7.838

Cause Analysis and Removal of Boundary Artifacts in Image Deconvolution  

Lee, Ji-Yeon (Department of Computer Aided Science, Inje University)
Lee, Nam-Yong (Department of Applied Mathematics, Inje University)
Publication Information
Journal of Korea Multimedia Society / v.17, no.7, 2014 , pp. 838-848 More about this Journal
Abstract
In this paper, we conducted a cause analysis on boundary artifacts in image deconvolution. Results of the cause analysis show that boundary artifacts are caused not only by a misuse of boundary conditions but also by no use of the normalized backprojection. Results also showed that the correct use of boundary conditions does not necessarily remove boundary artifacts. Based on these observations, we suggest not to use any specific boundary conditions and to use the normalized backprojector for boundary artifact-free image deconvolution.
Keywords
Landweber; Richardson-Lucy; Conjugate Gradient Method; Free Boundary Condition; Normalized Backprojector;
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1 M. Bertero and P. Boccacci, "A Simple Method for The Reduction of Boundary Effects in The Richardson-Lucy Approach to Image Deconvolution," Astronomy and Astrophysics, Vol. 437, No. 1, pp. 369-374, 2005.   DOI   ScienceOn
2 N.-Y. Lee and B. Lucier, Preconditioned Conjugate Gradient Method for Boundary Artifacts-free Image Deblurring, Technical Report 3-CNA-011, Center for Nonlinear Analysis, Carnegie Mellon University, 2013 (Submitted).
3 G. L. Zeng and C. T. Gullberg, "Unmatched Projector/Backprojector Pairs in an Iterative Reconstruction Algorithm," IEEE Transaction on Medical Imaging, Vol. 19, No. 5, pp. 548- 555, 2000.   DOI   ScienceOn
4 D. Calvetti, and E. Somersalo, "Bayesian Image Deblurring and Boundary Effects," Proceeding of Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 5910, pp. 281-289. 2005.
5 W. H. Richardson, "Baysian-based Iterative Method of Image Restoration," Journal of the Optical Society of America, Vol. 62, No. 1, pp. 55-59, 1972.   DOI
6 L. B. Lucy, "An Iterative Technique for The Rectification of Observed Distributions," The Astronomical Journal, Vol. 79, No. 6, pp. 745- 754, 1974.   DOI
7 D. Donoho, "Nonlinear Solution of Linear Inverse Problems by Wavelet-vagulette Decomposition," Applied and Computational Harmonic Analysis, Vol. 2, No. 2, pp. 101-126, 1995.   DOI
8 R. Chan, T. Chan, L. Shen, and Z. Shen, "Wavelet Deblurring Algorithms for Spatially Varying Blur from High-resolution Image Reconstruction," Linear Algebra and its Applications, Vol. 366, No. 1, pp.139-155, 2003.   DOI
9 R. Rudin and S. Osher, "Total Variation based Image Restoration with Free Local Constraints," Proceeding of IEEE International Conference Image Processing, Vol. 1. pp. 31-35, 1994.
10 M. Welk, D. Thesi, and J. Weickert, "Variational Deblurring of Images with Uncertain and Spatially Variant Blurs," Pattern Recognition, Vol. 3663, No. 1, pp. 485-492, 2005.
11 S.A. Yoon, T.G. Lee, S.H Lee, M.K. Son, D.G. Kim and C.H. Won "Image Resolution Enhancement by Improved S&A Method using POCS," Journal of Korea Multimedia Society, Vol. 14, No. 11, pp. 1392-1400, 2011.   과학기술학회마을   DOI
12 A. Tekalp and M. Sezan, "Quantitative Analysis of Artifacts in Linear Space-invariant Image Restoration," Multidimensional Systems and Signal Processing, Vol. 1, No. 2, pp. 143-177, 1990.   DOI
13 J. Nagy, K. Palmer, and L. Perrone, "Iterative Methods for Image Deblurring: A Matlab Oriented Approach," Numerical Algorithms, Vol. 36, No. 1, pp. 73-93, 2004.   DOI   ScienceOn
14 M. Ng, R. Chan, and W.-C. Tang, "A Fast Algorithm for Deblurring Models with Neumann Boundary Donditions," SIAM Journal on Scientific Computing, Vol. 21, No. 3, pp. 851-866, 1999.   DOI   ScienceOn
15 M. Hanke, J. Nagy, and R. Plemmons, "Preconditioned Iterative Regularization Methods for Ill-posed Problems," in Numerical Linear Algebra and Scientific Computing, eds. L. Reichel, pp. 141-163. de Gruyter, Berlin, Germany, 1993.
16 R. Gonzalez, and R. Woods. Digital Image Processing Prentice-Hall, Englewood Cliffs, NJ. 2002.
17 M. R. Hestenes and E. Stiefel, "Methods of Conjugate Gradients for Solving Linear Systems," Journal of Research of the National Bureau of Standards, Vol. 49, No. 6, pp. 409- 436, 1952.   DOI
18 S. Sera-Capizzano, "A Note on Anti-reflective Boundary Conditions and Fast Deblurring Models," SIAM Journal of Scientific Computing. Vol. 25, No. 4, 1307- 1325, 2003.
19 D. Calvetti, J. Kaipio, and E. Someralo, "Aristotelian prior Boundary Conditions," International Journal of Mathematics and Computer Science, Vol. 1, No. 1, pp. 63-81, 2006.
20 H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems, Kluwer Academic Publishers, Dordrecht, 2000.
21 S. Haykin. Adaptive Filtering Theory. Prentice- Hall, Inc. Upper Saddle River, NJ, USA.1986.