Bayesian-optimal image reconstruction for translational-symmetric filters

Satohiro Tajima, Masato Inoue, Masato Okada

    Research output: Contribution to journalArticle

    3 Citations (Scopus)

    Abstract

    Translational-symmetric filters provide a foundation for various kinds of image processing. When a filtered image containing noise is observed, the original one can be reconstructed by Bayesian inference. Furthermore, hyperparameters such as the smoothness of the image and the noise level in the communication channel through which the image observed can be estimated from the observed image by setting a criterion of maximizing marginalized likelihood. In this article we apply a diagonalization technique with the Fourier transform to this image reconstruction problem. This diagonalization not only reduces computational costs but also facilitates theoretical analyses of the estimation and reconstruction performances. We take as an example the Mexican-hat shaped neural cell receptive field seen in the early visual systems of animals, and we compare the reconstruction performances obtained under various hyperparameter and filter parameter conditions with each other and with the corresponding performances obtained under no-filter conditions. The results show that the using a Mexican-hat filter can reduce reconstruction error.

    Original languageEnglish
    Article number054803
    JournalJournal of the Physical Society of Japan
    Volume77
    Issue number5
    DOIs
    Publication statusPublished - 2008 May

    Fingerprint

    image reconstruction
    filters
    inference
    image processing
    animals
    communication
    costs
    cells

    Keywords

    • Bayesian inference
    • Denoising
    • Filter design
    • Fourier transform
    • Hyperparameter estimation
    • Image reconstruction
    • Translational invariance

    ASJC Scopus subject areas

    • Physics and Astronomy(all)

    Cite this

    Bayesian-optimal image reconstruction for translational-symmetric filters. / Tajima, Satohiro; Inoue, Masato; Okada, Masato.

    In: Journal of the Physical Society of Japan, Vol. 77, No. 5, 054803, 05.2008.

    Research output: Contribution to journalArticle

    @article{2f0478dd4f114058acdd555c11ad1861,
    title = "Bayesian-optimal image reconstruction for translational-symmetric filters",
    abstract = "Translational-symmetric filters provide a foundation for various kinds of image processing. When a filtered image containing noise is observed, the original one can be reconstructed by Bayesian inference. Furthermore, hyperparameters such as the smoothness of the image and the noise level in the communication channel through which the image observed can be estimated from the observed image by setting a criterion of maximizing marginalized likelihood. In this article we apply a diagonalization technique with the Fourier transform to this image reconstruction problem. This diagonalization not only reduces computational costs but also facilitates theoretical analyses of the estimation and reconstruction performances. We take as an example the Mexican-hat shaped neural cell receptive field seen in the early visual systems of animals, and we compare the reconstruction performances obtained under various hyperparameter and filter parameter conditions with each other and with the corresponding performances obtained under no-filter conditions. The results show that the using a Mexican-hat filter can reduce reconstruction error.",
    keywords = "Bayesian inference, Denoising, Filter design, Fourier transform, Hyperparameter estimation, Image reconstruction, Translational invariance",
    author = "Satohiro Tajima and Masato Inoue and Masato Okada",
    year = "2008",
    month = "5",
    doi = "10.1143/JPSJ.77.054803",
    language = "English",
    volume = "77",
    journal = "Journal of the Physical Society of Japan",
    issn = "0031-9015",
    publisher = "Physical Society of Japan",
    number = "5",

    }

    TY - JOUR

    T1 - Bayesian-optimal image reconstruction for translational-symmetric filters

    AU - Tajima, Satohiro

    AU - Inoue, Masato

    AU - Okada, Masato

    PY - 2008/5

    Y1 - 2008/5

    N2 - Translational-symmetric filters provide a foundation for various kinds of image processing. When a filtered image containing noise is observed, the original one can be reconstructed by Bayesian inference. Furthermore, hyperparameters such as the smoothness of the image and the noise level in the communication channel through which the image observed can be estimated from the observed image by setting a criterion of maximizing marginalized likelihood. In this article we apply a diagonalization technique with the Fourier transform to this image reconstruction problem. This diagonalization not only reduces computational costs but also facilitates theoretical analyses of the estimation and reconstruction performances. We take as an example the Mexican-hat shaped neural cell receptive field seen in the early visual systems of animals, and we compare the reconstruction performances obtained under various hyperparameter and filter parameter conditions with each other and with the corresponding performances obtained under no-filter conditions. The results show that the using a Mexican-hat filter can reduce reconstruction error.

    AB - Translational-symmetric filters provide a foundation for various kinds of image processing. When a filtered image containing noise is observed, the original one can be reconstructed by Bayesian inference. Furthermore, hyperparameters such as the smoothness of the image and the noise level in the communication channel through which the image observed can be estimated from the observed image by setting a criterion of maximizing marginalized likelihood. In this article we apply a diagonalization technique with the Fourier transform to this image reconstruction problem. This diagonalization not only reduces computational costs but also facilitates theoretical analyses of the estimation and reconstruction performances. We take as an example the Mexican-hat shaped neural cell receptive field seen in the early visual systems of animals, and we compare the reconstruction performances obtained under various hyperparameter and filter parameter conditions with each other and with the corresponding performances obtained under no-filter conditions. The results show that the using a Mexican-hat filter can reduce reconstruction error.

    KW - Bayesian inference

    KW - Denoising

    KW - Filter design

    KW - Fourier transform

    KW - Hyperparameter estimation

    KW - Image reconstruction

    KW - Translational invariance

    UR - http://www.scopus.com/inward/record.url?scp=54349116519&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=54349116519&partnerID=8YFLogxK

    U2 - 10.1143/JPSJ.77.054803

    DO - 10.1143/JPSJ.77.054803

    M3 - Article

    AN - SCOPUS:54349116519

    VL - 77

    JO - Journal of the Physical Society of Japan

    JF - Journal of the Physical Society of Japan

    SN - 0031-9015

    IS - 5

    M1 - 054803

    ER -