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Mirrored mixture PDF models for scientific image modelling

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Abstract

This paper deals with the modelling of high bit-depth images acquired by astronomical cameras using the discrete wavelet transform and the undecimated discrete wavelet transform for image representation. The probability density function (PDF) model parameters are estimated using the expectation-maximization (EM) algorithm and the method of moments. As proposed in this paper, the task of estimating the overall PDF model parameters can be simplified by so-called mirroring of the initial model which is estimated only for those wavelet coefficients that are greater than or equal to zero. In the case of the EM algorithm, this technique significantly reduces the computational cost of the model fitting algorithm. In our experiments, we achieved a reduction of more than 70%. In the case of the method of moments, this technique simplifies a system of moment equations. Three main PDF models are presented here: firstly, the mirrored mixture of a half-normal distribution and an exponential distribution, secondly, the mirrored mixture of two exponential distributions, and finally, the mirrored mixture of two half-normal distributions. Performance of these models is evaluated on three sets of astronomical images and also on artificial data using the Jeffrey divergence metric. Overall, the mirrored mixture of a half-normal and an exponential distribution overcomes the commonly used GLM (generalized Laplacian model) and also the other studied models.

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Acknowledgements

This work has been supported by the grant GA17-05840S ”Multicriteria Optimization of Shift-Variant Imaging System Models” of the Czech Science Foundation.

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  1. Department of Radioelectronics, Czech Technical University in Prague, Prague, Czech Republic

    Jan Švihlík

  2. Department of Computing and Control Engineering, University of Chemistry and Technology, Prague, Czech Republic

    Jan Švihlík

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  1. Jan Švihlík
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Correspondence to Jan Švihlík.

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Švihlík, J. Mirrored mixture PDF models for scientific image modelling. SIViP 16, 385–393 (2022). https://doi.org/10.1007/s11760-021-01944-z

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