Bayesian-optimal image reconstruction for translational-symmetric filters

Satohiro Tajima*, Masato Inoue, Masato Okada

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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
Issue number5
Publication statusPublished - 2008 May 1


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

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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