Bayesian-Optimal Image Reconstruction for Translational-Symmetric Filters

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  • Tajima Satohiro
    Department of Complexity Science and Engineering, Graduate School of Frontier Sciences, The University of Tokyo
  • Inoue Masato
    Department of Electrical Engineering and Bioscience, School of Science and Engineering, Waseda University
  • Okada Masato
    Department of Complexity Science and Engineering, Graduate School of Frontier Sciences, The University of Tokyo RIKEN Brain Science Institute

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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.

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