Abstract
Matched filters are revisited from the ciewpoint of regulations of the ill-posed problem and the super-resolution. Object-matched minimum mean-square image spread (MMIS) filters are derived from a general contrained moment expansion method. An inverse problem of image processing is to determine an optimum trade-off potential U\([(\overrightarrow f )\) or V\([(\overrightarrow f )\) from the knowledge of the restored object Q\([(\overrightarrow f )\) or the output transfer function Ψ\([(\overrightarrow f )\) as S\([(\overrightarrow f )\). Analytic example and exact solutions are given for the coherent and incoherent image restorations. A MMIS filter is found to yield an identical minimum mean square estimation-error (MMSE) filter of Wiener in the special case, similar to the visual MTF or contrast sensitivity function, peaked at the middle band of spatial frequency channels. The direct problem for the linear and noisy motion-blurred image restoration is solved. By means of the Gelf fand-Levitan inverse transform technique for the reference potential, the inverse problem is solved and the design of the energy constrained WES filter follows. Finally, both the direct and inverse problems are exemplified with the dc-incision, namely the central dark field method of Abbe and Zernike, useful for a systematical design of both the imaging OTF and linage restoration filters under noise. The simple rule of thumb is given for mannnade sciences.
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© 1985 D. Reidel Publishing Company
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Szu, H.H. (1985). Image Processing: Analysis Beyond Matched Filtering. In: Boerner, WM., et al. Inverse Methods in Electromagnetic Imaging. NATO ASI Series, vol 143. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5271-3_27
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DOI: https://doi.org/10.1007/978-94-009-5271-3_27
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