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Mirrored mixture PDF models for scientific image modelling
Signal, Image and Video Processing ( IF 2.3 ) Pub Date : 2021-06-12 , DOI: 10.1007/s11760-021-01944-z
Jan Švihlík

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.



中文翻译:

用于科学图像建模的镜像混合 PDF 模型

本文使用离散小波变换和未抽取的离散小波变换对天文相机获取的高位深度图像进行建模以进行图像表示。使用期望最大化 (EM) 算法和矩量法估计概率密度函数 (PDF) 模型参数。正如本文所提出的,估计整体 PDF 模型参数的任务可以通过所谓的初始模型镜像来简化,该初始模型仅针对那些大于或等于 0 的小波系数进行估计。在 EM 算法的情况下,该技术显着降低了模型拟合算法的计算成本。在我们的实验中,我们实现了 70% 以上的减少。在矩量法的情况下,这种技术简化了力矩方程系统。这里介绍了三个主要的 PDF 模型:首先,半正态分布和指数分布的镜像混合,其次,两个指数分布的镜像混合,最后,两个半正态分布的镜像混合。这些模型的性能在三组天文图像以及使用 Jeffrey 散度度量的人工数据上进行评估。总体而言,半正态分布和指数分布的镜像混合克服了常用的 GLM(广义拉普拉斯模型)以及其他研究模型。最后,两个半正态分布的镜像混合。这些模型的性能在三组天文图像以及使用 Jeffrey 散度度量的人工数据上进行评估。总体而言,半正态分布和指数分布的镜像混合克服了常用的 GLM(广义拉普拉斯模型)以及其他研究模型。最后,两个半正态分布的镜像混合。这些模型的性能在三组天文图像以及使用 Jeffrey 散度度量的人工数据上进行评估。总体而言,半正态分布和指数分布的镜像混合克服了常用的 GLM(广义拉普拉斯模型)以及其他研究模型。

更新日期:2021-06-13
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