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A Variational Approach to Reconstructing Images Corrupted by Poisson Noise

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Abstract

We propose a new variational model to denoise an image corrupted by Poisson noise. Like the ROF model described in [1] and [2], the new model uses total-variation regularization, which preserves edges. Unlike the ROF model, our model uses a data-fidelity term that is suitable for Poisson noise. The result is that the strength of the regularization is signal dependent, precisely like Poisson noise. Noise of varying scales will be removed by our model, while preserving low-contrast features in regions of low intensity.

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Authors and Affiliations

  1. Department of Mathematics, Yale University, P.O. Box 208283, New Haven, CT, 06520-8283

    Triet Le

  2. Los Alamos National Laboratory, Theoretical Division, MS B284, Los Alamos, NM, 87545

    Rick Chartrand

  3. Los Alamos National Laboratory, Computer and Computational Sciences Division, MS D413, Los Alamos, NM, 87545

    Thomas J. Asaki

Authors
  1. Triet Le
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  2. Rick Chartrand
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  3. Thomas J. Asaki
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Corresponding author

Correspondence to Triet Le.

Additional information

Funded by the Department of Energy under contract W-7405ENG-36.

Triet M. Le received his Ph.D. in Mathematics from the University of California, Los Angeles, in 2006. He is now a Gibbs Assistant Professor in the Mathematics Department at Yale University. His research interests are in applied harmonic analysis and function spaces with application to image analysis and inverse problems.

Rick Chartrand received a Ph.D. in Mathematics from UC Berkeley in 1999, where he studied functional analysis. He now works as an applied mathematician at Los Alamos National Laboratory. His research interests are image and signal processing, inverse problems, and classification.

Tom Asaki is a staff member in the Computer and Computational Science Division at Los Alamos National Laboratory. He obtained his doctorate in physics from Washington State University. His interests are mixed-variable and direct-search optimization, applied inverse problems, and quantitative tomography.

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Le, T., Chartrand, R. & Asaki, T.J. A Variational Approach to Reconstructing Images Corrupted by Poisson Noise. J Math Imaging Vis 27, 257–263 (2007). https://doi.org/10.1007/s10851-007-0652-y

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  • DOI: https://doi.org/10.1007/s10851-007-0652-y

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