Abstract
This paper considers the application of the method of regularisation within the context of the restoration of degraded two-dimensional images. In particular, several recipes for choosing an appropriate degree of regularisation are described and their performance compared with reference to test-images. Some of these methods require the availability of a data-based noise-estimator; a neighbourhood noise estimator is proposed and its performance is discussed.
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References
T. Poggio, V. Torre and C. Koch (1985). Computational Vision and Regularisation Theory. Nature, Vol. 317, 314–319.
D.S. Sharman, K.A. Stewart and T.S. Durrani (1986). The use of Context in Image Restoration. Presented at the BPRA (Scotland) conference on Adaptive Image Analysis at Heriot-Watt University, May, 1986.
A.R. Davies and R.S. Anderssen (1986). Optimisation in the Regularisation of Ill-posed Problems. Journal of the Australian Mathematical Soceity (Series B), 28, 114–133.
D.M. Titterington (1985). Common Structure of Smoothing Techniques in Statistics. International Statistical Review, 53, 141–70.
P. Craven and G. Wahba (1979). Smoothing Noisy Data with spline functions: estimating the correct degree of smoothing by the method of generalised cross-validation. Number. Math., 31, 377–403.
A.M. Thompson, J.C. Brown, J.W. Kay and D.M. Titterington (1987). A comparison of methods of choosing the smoothing parameter in image restoration by regularisation. In preparation.
C.W. Groetsch. The Theory of Tikhonov regularisation for Fredholm equations of the first kind. Research Notes in Mathematics No.105, Pitman.
P. Hall and D.M. Titterington (1987). Common structure of techniques for choosing smoothing parameters in regression problems. J.R. Statist. Soc. B., 49, No.2, 184–198.
P. Hall and D.M. Titterington (1986). On some Smoothing Techniques used in Image Restoration. J.R. Statist. Soc., 48, No. 3, 330–343.
V.F. Turchin (1967). Solution of the Fredholm equation of the first kind in a statistical ensemble of smooth functions. USSR Comp. Math. and Math. Phys., 7, 79–96.
V.F. Turchin (1968). Selection of an ensemble of smooth functions for the solution of the inverse problem. USSR Comput. Math. and Math. Phys., 8, 328–339.
G.H. Golub, M. Heath and G. Wahba (1979). Generalised cross-validation as a method for choosing a good ridge parameter. Technometrics, 21, 215–223. validation as a method for choosing a good ridge parameter. Technometrics, 21, 215–223.
A.K. Jain (1978). Fast Inversion of Banded Toeplitz Matrices by Circular Decompositions. IEEE Trans. A.S.S.P., Vol. ASSP-26, No. 2, 1978.
R.C. Gonzales & P. Wintz (1987). Digital Image Processing. Second Edition. Addison-Wesley.
R.M. Gray. On the Asymptotic Eigenvalue Distribution of Toeplitz Matrices. IEEE Trans. Inf. Th., Vol. IT-18, No. 6, Nov. 1972.
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© 1988 Springer-Verlag Berlin Heidelberg
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Kay, J.W. (1988). On the choice of regularisation parameter in image restoration. In: Kittler, J. (eds) Pattern Recognition. PAR 1988. Lecture Notes in Computer Science, vol 301. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-19036-8_59
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DOI: https://doi.org/10.1007/3-540-19036-8_59
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