Abstract
Algorithms for computing optimally regularized solutions of first kind integral equations under non-negativity constraints necessarily require far more computer time than algorithms which do not implement such constraints, particularly in higher dimensions. Whenever the structure of the kernel of the integral equation allows, therefore, it is important to take full advantage of special properties to maximize efficiency. In this paper we shall present some ideas for improving efficiency in the case of non-negatively constrained deconvolution problems. The algorithm we propose to modify is originally due to Wahba [1], and uses quadratic programming to achieve constrained Tikhonov regularization while using cross-validation to optimize the regularization parameter.
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References
G. Wahba. Constrained regularization for ill-posed operator equations, with applications in meteorology and medicine. In Ststistical Decision Theory and Related Topics III, Vol. 2, eds. S.S. Gupta and J. O. Bergen (Academic Press, New York ) 1982.
A. R. Davies and R. S. Anderssen. J. Aust. Math. Soc. Ser. B, 28 (1986) 114–133.
A. R. Davies and M. F. Hassan. Optimality in the regularization of ill-posed inverse problems. In Inverse Problems: An Interdisciplinary Study, ed. P. C. Sabatier ( Academic Press, London ) 1987, pp 553–562.
R. Fletcher. Practical Methods of Optimization, Vol. 2. John Wiley, Chichester. 1981.
R. H. Chan and G. Strang. The asymptotic Toeplitz-Circulant eigenvalue problem. Research Report, CMA-R21-87. Centre for Mathematical Analysis, Australian National University.
M. Iqbal. The Numerical Solution of Fredholm Integral Equations of the First Kind. Ph.D. Thesis, University of Wales. 1989.
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© 1990 Springer-Verlag Berlin Heidelberg
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Davies, A.R. (1990). Circulant Preconditioners for Non-negatively Constrained Deconvolution Problems. In: Sabatier, P.C. (eds) Inverse Methods in Action. Inverse Problems and Theoretical Imaging. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-75298-8_11
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DOI: https://doi.org/10.1007/978-3-642-75298-8_11
Publisher Name: Springer, Berlin, Heidelberg
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