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Restoring with Maximum Likelihood and Maximum Entropy*
Abstract
Given M sampled image values of an incoherent object, what can be deduced as the most likely object? Using a communication-theory model for the process of image formation, we find that the most likely object has a maximum entropy and is represented by a restoring formula that is positive and not band limited. The derivation is an adaptation to optics of a formulation by Jaynes for unbiased estimates of positive probability functions. The restoring formula is tested, via computer simulation, upon noisy images of objects consisting of random impulses. These are found to be well restored, with resolution often exceeding the Rayleigh limit and with a complete absence of spurious detail. The proviso is that the noise in each image input must not exceed about 40% of the signal image. The restoring method is applied to experimental data consisting of line spectra. Results are consistent with those of the computer simulations.
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Cited by
Stochastic relaxation, gibbs distributions, and the bayesian restoration of images.
Geman, S., & Geman, D. (1984) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.1984.4767596 · Cited by 17,949
Image reconstruction from incomplete and noisy data
Gull, S. F., & Daniell, G. J. (1978) · Nature · doi:10.1038/272686a0 · Cited by 965
From Laplace to Supernova SN 1987A: Bayesian Inference in Astrophysics
Loredo, T. J. (1990) · Maximum Entropy and Bayesian Methods · doi:10.1007/978-94-009-0683-9_6 · Cited by 168
Variational Image Feature Extraction for the Event Horizon Telescope
Tiede, P., Broderick, A. E., & Palumbo, D. C. M. (2022) · The Astrophysical Journal · doi:10.3847/1538-4357/ac3a6b · Cited by 29
Metadata
- Authors
- Frieden, B. R.
- Venue
- Journal of the Optical Society of America
- Publisher
- Optica Publishing Group
- Published
- 1972-04-01
- Volume
- 62
- Issue
- 4
- Pages
- 511
- ISSN
- 0030-3941 (ISSN-L)
- OpenAlex
- W2078403926
- Cited by
- 638
- References
- 0
- FWCI
- 10.20
- Type
- journal article
- Language
- en
- Open access
- closed
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- Frieden, B. R. (1972). Restoring with Maximum Likelihood and Maximum Entropy*. Journal of the Optical Society of America. https://doi.org/10.1364/josa.62.000511
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