Wavelet-based Bayesian Estimator for Poisson Noise Removal from Images

Xu Huang, A Madoc, Andrew Cheetham

    Research output: A Conference proceeding or a Chapter in BookConference contribution

    11 Citations (Scopus)
    1 Downloads (Pure)

    Abstract

    Images are, in many cases, degraded even before they are encoded. Emission and transmission tomography images, X-ray films, and photographs taken by satellites are usually contaminated by quantum noise, which is Poisson distributed. Poisson shot noise is a natural generalization of a compound Poisson process when the summands are stochastic processes starting at the points of the underlying Poisson process. Unlike additive Gaussian noise, Poisson noise is signal-dependent and separating signal from noise is a difficult task. A wavelet-based maximum likelihood for a Bayesian estimator that recovers the signal component of the wavelet coefficients in original images by using an alpha-stable signal prior distribution is extended to the Poisson noise removal from a previous investigation. As we discussed in our earlier papers that Bayesian estimator can approximate impulsive noise more accurately than other models and that in the general case the Bayesian processor does not have a closed-form expression. The parameters relative to Bayesian estimators of the model are carefully investigated after an investigation of a-stable simulations for a maximum likelihood estimator. As an example, an improved Bayesian estimator that is a natural extension of other wavelet denoising (soft and hard threshold methods) via a colour image is presented to illustrate our discussion.
    Original languageEnglish
    Title of host publicationProceedings: 2003 IEEE International Conference on Multimedia and Expo
    EditorsK.J Ray Liu
    Place of PublicationUSA
    PublisherIEEE
    Pages593-596
    Number of pages4
    ISBN (Print)0-7803-7965-9
    DOIs
    Publication statusPublished - 2003
    Event2003 IEEE International Conference on Multimedia & Expo - Baltimore, United States
    Duration: 6 Jul 20039 Jul 2003

    Conference

    Conference2003 IEEE International Conference on Multimedia & Expo
    CountryUnited States
    CityBaltimore
    Period6/07/039/07/03

    Fingerprint

    estimators
    poisson process
    stochastic processes
    shot noise
    random noise
    photographs
    central processing units
    tomography
    color
    thresholds
    coefficients
    x rays
    simulation

    Cite this

    Huang, X., Madoc, A., & Cheetham, A. (2003). Wavelet-based Bayesian Estimator for Poisson Noise Removal from Images. In K. J. R. Liu (Ed.), Proceedings: 2003 IEEE International Conference on Multimedia and Expo (pp. 593-596). USA: IEEE. https://doi.org/10.1109/ICME.2003.1220987
    Huang, Xu ; Madoc, A ; Cheetham, Andrew. / Wavelet-based Bayesian Estimator for Poisson Noise Removal from Images. Proceedings: 2003 IEEE International Conference on Multimedia and Expo. editor / K.J Ray Liu. USA : IEEE, 2003. pp. 593-596
    @inproceedings{f819614534c2454a9609b51d67b725df,
    title = "Wavelet-based Bayesian Estimator for Poisson Noise Removal from Images",
    abstract = "Images are, in many cases, degraded even before they are encoded. Emission and transmission tomography images, X-ray films, and photographs taken by satellites are usually contaminated by quantum noise, which is Poisson distributed. Poisson shot noise is a natural generalization of a compound Poisson process when the summands are stochastic processes starting at the points of the underlying Poisson process. Unlike additive Gaussian noise, Poisson noise is signal-dependent and separating signal from noise is a difficult task. A wavelet-based maximum likelihood for a Bayesian estimator that recovers the signal component of the wavelet coefficients in original images by using an alpha-stable signal prior distribution is extended to the Poisson noise removal from a previous investigation. As we discussed in our earlier papers that Bayesian estimator can approximate impulsive noise more accurately than other models and that in the general case the Bayesian processor does not have a closed-form expression. The parameters relative to Bayesian estimators of the model are carefully investigated after an investigation of a-stable simulations for a maximum likelihood estimator. As an example, an improved Bayesian estimator that is a natural extension of other wavelet denoising (soft and hard threshold methods) via a colour image is presented to illustrate our discussion.",
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    language = "English",
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    booktitle = "Proceedings: 2003 IEEE International Conference on Multimedia and Expo",
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    Huang, X, Madoc, A & Cheetham, A 2003, Wavelet-based Bayesian Estimator for Poisson Noise Removal from Images. in KJR Liu (ed.), Proceedings: 2003 IEEE International Conference on Multimedia and Expo. IEEE, USA, pp. 593-596, 2003 IEEE International Conference on Multimedia & Expo, Baltimore, United States, 6/07/03. https://doi.org/10.1109/ICME.2003.1220987

    Wavelet-based Bayesian Estimator for Poisson Noise Removal from Images. / Huang, Xu; Madoc, A; Cheetham, Andrew.

    Proceedings: 2003 IEEE International Conference on Multimedia and Expo. ed. / K.J Ray Liu. USA : IEEE, 2003. p. 593-596.

    Research output: A Conference proceeding or a Chapter in BookConference contribution

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    T1 - Wavelet-based Bayesian Estimator for Poisson Noise Removal from Images

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    AU - Madoc, A

    AU - Cheetham, Andrew

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    N2 - Images are, in many cases, degraded even before they are encoded. Emission and transmission tomography images, X-ray films, and photographs taken by satellites are usually contaminated by quantum noise, which is Poisson distributed. Poisson shot noise is a natural generalization of a compound Poisson process when the summands are stochastic processes starting at the points of the underlying Poisson process. Unlike additive Gaussian noise, Poisson noise is signal-dependent and separating signal from noise is a difficult task. A wavelet-based maximum likelihood for a Bayesian estimator that recovers the signal component of the wavelet coefficients in original images by using an alpha-stable signal prior distribution is extended to the Poisson noise removal from a previous investigation. As we discussed in our earlier papers that Bayesian estimator can approximate impulsive noise more accurately than other models and that in the general case the Bayesian processor does not have a closed-form expression. The parameters relative to Bayesian estimators of the model are carefully investigated after an investigation of a-stable simulations for a maximum likelihood estimator. As an example, an improved Bayesian estimator that is a natural extension of other wavelet denoising (soft and hard threshold methods) via a colour image is presented to illustrate our discussion.

    AB - Images are, in many cases, degraded even before they are encoded. Emission and transmission tomography images, X-ray films, and photographs taken by satellites are usually contaminated by quantum noise, which is Poisson distributed. Poisson shot noise is a natural generalization of a compound Poisson process when the summands are stochastic processes starting at the points of the underlying Poisson process. Unlike additive Gaussian noise, Poisson noise is signal-dependent and separating signal from noise is a difficult task. A wavelet-based maximum likelihood for a Bayesian estimator that recovers the signal component of the wavelet coefficients in original images by using an alpha-stable signal prior distribution is extended to the Poisson noise removal from a previous investigation. As we discussed in our earlier papers that Bayesian estimator can approximate impulsive noise more accurately than other models and that in the general case the Bayesian processor does not have a closed-form expression. The parameters relative to Bayesian estimators of the model are carefully investigated after an investigation of a-stable simulations for a maximum likelihood estimator. As an example, an improved Bayesian estimator that is a natural extension of other wavelet denoising (soft and hard threshold methods) via a colour image is presented to illustrate our discussion.

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    Huang X, Madoc A, Cheetham A. Wavelet-based Bayesian Estimator for Poisson Noise Removal from Images. In Liu KJR, editor, Proceedings: 2003 IEEE International Conference on Multimedia and Expo. USA: IEEE. 2003. p. 593-596 https://doi.org/10.1109/ICME.2003.1220987