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Cited by 393

The DOI matches its Crossref record; 36 of the 36 references it cites were found in a registry or an index.

Maximum Entropy and the Nearly Black Object

Donoho, David L., Johnstone, Iain M., Hoch, Jeffrey C., Stern, Alan S.·1992·Journal of the Royal Statistical Society Series B: Statistical Methodology

Abstract

SUMMARY: Maximum entropy (ME) inversion is a non-linear inversion technique for inverse problems where the object to be recovered is known to be positive. It has been applied in areas ranging from radio astronomy to various forms of spectroscopy, sometimes with dramatic success. In some cases, ME has attained an order of magnitude finer resolution and/or an order of magnitude smaller noise level than that obtainable by standard linear methods. The dramatic successes all seem to occur in cases where the object to be recovered is ‘nearly black‘: essentially zero in the vast majority of samples. We show that near-blackness is required, both for signal-to-noise enhancements and for superresolution. However, other methods—in particular, minimum l 1-norm reconstruction—may exploit near-blackness to an even greater extent.

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Cites

Show all 36 references

Research works printed but not linked: 24

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  4. Donoho, 1988, One-sided inference about functionals of a density, Ann. Statist., 16, 1390, 10.1214/aos/1176351045 · doi:10.1214/aos/1176351045
  5. Donoho, 1990, Super-resolution via sparsity constraints
  6. Donoho, 1989, Minimax risk over lp balls
  7. Donoho, 1991, Superresolution and positivity constraints: theory and experiment
  8. Donoho, 1990, Does maximum entropy improve sensitivity?, Proc. Natn. Acad. Sci. USA, 87, 5066, 10.1073/pnas.87.13.5066 · doi:10.1073/pnas.87.13.5066
  9. Freeman, 1988, A Handbook of Nuclear Magnetic Resonance.
  10. Frieden, 1972, Restoring with Maximum Entropy: II, Superresolution of photographs with diffraction-blurred impulses, J. Opt. Soc. Am., 62, 1202, 10.1364/JOSA.62.001202 · doi:10.1364/josa.62.001202
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  12. Harwit, 1979, Hadamard Transform Optics.
  13. Hoch, 1989, Reconstruction of complex, phase-sensitive spectra, J. Magn. Resnce, 86, 236
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  15. Logan, 1965, Properties of high-pass signals
  16. Narayan, 1982, Maximum entropy image reconstruction—a practical, non-information theoretical approach, J. Astrophys., 3, 419
  17. Newman, 1988, Maximization of entropy and minimization of area as criteria for NMR signal processing, J. Magn. Resnce, 79, 448
  18. Pinsker, 1980, Optimal filtration of square-integrable signals in Gaussian white noise, Prob. Inform. Transmissn, 16, 120
  19. Redfearn, 1984, The Times
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  23. Titterington, 1984, The maximum entropy method for data analysis, Nature, 312, 381, 10.1038/312381b0 · doi:10.1038/312381b0
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Metadata

Authors
Donoho, D. L., Johnstone, I. M., Hoch, J. C., & Stern, A. S.
Venue
Journal of the Royal Statistical Society Series B: Statistical Methodology
Published
1992-09-01
Volume
54
Issue
1
Pages
41-67
ISSN
  • 1369-7412 (ISSN-L)
  • 1467-9868
OpenAlex
W129423020
Cited by
393
References
36
FWCI
7.92
Type
journal article
Language
en
Open access
closed

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CoChat. (2026). Citation check: Maximum Entropy and the Nearly Black Object. https://app.cochat.ai/papers/10.1111/j.2517-6161.1992.tb01864.x
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Donoho, D. L., Johnstone, I. M., Hoch, J. C., & Stern, A. S. (1992). Maximum Entropy and the Nearly Black Object. Journal of the Royal Statistical Society Series B: Statistical Methodology. https://doi.org/10.1111/j.2517-6161.1992.tb01864.x

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