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April, 1990 Optimal Convergence Rates in Signal Recovery
Peter Hall
Ann. Probab. 18(2): 887-900 (April, 1990). DOI: 10.1214/aop/1176990865


In the context of image analysis, the method of Fourier-domain processing is shown to yield restored signals of optimal quality. This confirms conjectures of statistical optimality that have been made in the past. Quality is measured in terms of convergence rates, and the influence of image smoothness on convergence rates is quantified. This influence is particularly interesting in the case of motion blur, where there is a critical degree of image smoothness (approximately four derivatives of the image) beyond which no improvement in restored image quality may be obtained by passing to smoother images. That is in marked contrast to the case of out-of-focus blur, where restored image quality is always greater for smoother images.


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Peter Hall. "Optimal Convergence Rates in Signal Recovery." Ann. Probab. 18 (2) 887 - 900, April, 1990.


Published: April, 1990
First available in Project Euclid: 19 April 2007

zbMATH: 0709.60048
MathSciNet: MR1055440
Digital Object Identifier: 10.1214/aop/1176990865

Primary: 60G35
Secondary: 62G05

Keywords: Blur , Convergence rates , image processing , image restoration , pointspread function , signal processing

Rights: Copyright © 1990 Institute of Mathematical Statistics


Vol.18 • No. 2 • April, 1990
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