An Additive Approximation to Multiplicative Noise
Multiplicative noise models are often used instead of additive noise models in cases in which the noise variance depends on the state. Furthermore, when Poisson distributions with relatively small counts are approximated with normal distributions, multiplicative noise approximations are straightforw...
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Veröffentlicht in: | Journal of mathematical imaging and vision 2020-11, Vol.62 (9), p.1227-1237 |
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description | Multiplicative noise models are often used instead of additive noise models in cases in which the noise variance depends on the state. Furthermore, when Poisson distributions with relatively small counts are approximated with normal distributions, multiplicative noise approximations are straightforward to implement. There are a number of limitations in the existing approaches to deal with multiplicative errors, such as positivity of the multiplicative noise term. The focus in this paper is on large dimensional (inverse) problems for which sampling-type approaches have too high computational complexity. In this paper, we propose an alternative approach utilising the Bayesian framework to carry out approximative marginalisation over the multiplicative error by embedding the statistics in an additive error term. The Bayesian framework allows the statistics of the resulting additive error term to be found based on the statistics of the other unknowns. As an example, we consider a deconvolution problem on random fields with different statistics of the multiplicative noise. Furthermore, the approach allows for correlated multiplicative noise. We show that the proposed approach provides feasible error estimates in the sense that the posterior models support the actual image. |
doi_str_mv | 10.1007/s10851-020-00984-3 |
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The Bayesian framework allows the statistics of the resulting additive error term to be found based on the statistics of the other unknowns. As an example, we consider a deconvolution problem on random fields with different statistics of the multiplicative noise. Furthermore, the approach allows for correlated multiplicative noise. 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P.</creatorcontrib><title>An Additive Approximation to Multiplicative Noise</title><title>Journal of mathematical imaging and vision</title><addtitle>J Math Imaging Vis</addtitle><description>Multiplicative noise models are often used instead of additive noise models in cases in which the noise variance depends on the state. Furthermore, when Poisson distributions with relatively small counts are approximated with normal distributions, multiplicative noise approximations are straightforward to implement. There are a number of limitations in the existing approaches to deal with multiplicative errors, such as positivity of the multiplicative noise term. The focus in this paper is on large dimensional (inverse) problems for which sampling-type approaches have too high computational complexity. In this paper, we propose an alternative approach utilising the Bayesian framework to carry out approximative marginalisation over the multiplicative error by embedding the statistics in an additive error term. The Bayesian framework allows the statistics of the resulting additive error term to be found based on the statistics of the other unknowns. As an example, we consider a deconvolution problem on random fields with different statistics of the multiplicative noise. Furthermore, the approach allows for correlated multiplicative noise. 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Furthermore, when Poisson distributions with relatively small counts are approximated with normal distributions, multiplicative noise approximations are straightforward to implement. There are a number of limitations in the existing approaches to deal with multiplicative errors, such as positivity of the multiplicative noise term. The focus in this paper is on large dimensional (inverse) problems for which sampling-type approaches have too high computational complexity. In this paper, we propose an alternative approach utilising the Bayesian framework to carry out approximative marginalisation over the multiplicative error by embedding the statistics in an additive error term. The Bayesian framework allows the statistics of the resulting additive error term to be found based on the statistics of the other unknowns. As an example, we consider a deconvolution problem on random fields with different statistics of the multiplicative noise. 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subjects | Applications of Mathematics Atmospheric pressure Bayesian analysis Computer Science Fields (mathematics) Image Processing and Computer Vision Mathematical Methods in Physics Noise Poisson distribution Signal,Image and Speech Processing Statistics |
title | An Additive Approximation to Multiplicative Noise |
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