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.

在噪声方差取决于状态的情况下，经常使用乘法噪声模型代替加性噪声模型。此外，当用正态分布来近似计数相对较小的泊松分布时，可以很容易地实现乘法噪声近似。现有的处理乘法误差的方法有很多限制，例如乘法噪声项的正性。本文的重点是样本类型方法的计算复杂度过高的大尺寸（逆）问题。在本文中，我们提出了一种替代方法，该方法利用贝叶斯框架将统计量嵌入附加误差项中，从而对乘法误差进行近似边缘化。贝叶斯框架允许基于其他未知数的统计来找到结果加性误差项的统计。举例来说，我们考虑具有不同乘性噪声统计量的随机场上的反卷积问题。此外，该方法允许相关的乘性噪声。我们表明，在后验模型支持实际图像的意义上，提出的方法提供了可行的误差估计。