9 November 1993 Zero estimation for blind deconvolution from noisy sampled data
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Abstract
Two- and higher-dimensional bandlimited functions are almost always non-factorizable, meaning that their zeros form a single analytic curve. In principle one can use this property to separate the product of two bandlimited functions into its respective factors; this is important in Fourier phase retrieval and deconvolution problems. The intersection of this zero structure with the real plane is at points, closed curves or lines stretching to infinity. The location of zero points, curves or lines can only be estimated, in practice, from available noisy data. The estimated locations can be used to write a factorizable approximation to the original function and we explore the consequences of doing this. Of importance is the fact that point zeros can be used to represent a 2D bandlimited function. Hence from intensity data, point zero locations in the intensity can be used directly to estimate the complex spectrum and provide an approximate solution to the phase retrieval problem. Examples will be given and their importance for the general blind deconvolution problem discussed.
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Pi-Tung Chen, Pi-Tung Chen, Michael A. Fiddy, Michael A. Fiddy, Alain H. Greenaway, Alain H. Greenaway, Yuanjie Wang, Yuanjie Wang, } "Zero estimation for blind deconvolution from noisy sampled data", Proc. SPIE 2029, Digital Image Recovery and Synthesis II, (9 November 1993); doi: 10.1117/12.161996; https://doi.org/10.1117/12.161996
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