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On Some Smoothing Techniques Used in Image Restoration

Peter Hall and D. M. Titterington
Journal of the Royal Statistical Society. Series B (Methodological)
Vol. 48, No. 3 (1986), pp. 330-343
Published by: Wiley for the Royal Statistical Society
Stable URL: http://www.jstor.org/stable/2345430
Page Count: 14
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On Some Smoothing Techniques Used in Image Restoration
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Abstract

The problem is considered of restoring a blurred and/or noisy image using various regularization prescriptions. Preliminary work concerns the invertibility of point spread functions and the construction of a stochastic model for images. A simple linear regularization procedure is introduced, as well as the special cases of constrained deconvolution, maximum entropy restoration and least-squares filtering. Optimal choices for the degree of smoothing are obtained for the case of low noise-to-signal ratios. Certain techniques, prevalent in the image-restoration literature for choosing the degree of smoothing, are shown to oversmooth, in a well-defined sense.

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