论文标题
完全自适应贝叶斯算法用于数据分析，Fabada
Fully Adaptive Bayesian Algorithm for Data Analysis, FABADA
论文作者
论文摘要
本文的目的是从贝叶斯推论的角度描述一种新型的非参数降噪技术，该技术可能会自动改善一维数据和二维数据的信噪比，例如天文图像和光谱。该算法迭代评估数据的平滑版本，平滑模型，从统计学上兼容与噪声测量值兼容的基础信号的估计。迭代基于证据和上一个平滑模型的$χ^2 $统计量停止，我们计算信号的期望值作为整个平滑模型的加权平均值。在本文中，我们解释了该算法的数学形式主义和数值实现，并使用一系列真实的天文观测来评估其在峰信号与噪声比，结构相似性指数和时间有效载荷方面评估其性能。我们用于数据分析的完全自适应贝叶斯算法（FABADA）产生的结果，没有任何参数调整，与标准图像处理算法相当，其参数已根据要恢复的真实信号进行了优化，这在实际应用中是不可能的。最先进的非参数方法（例如BM3D）在高信噪比下的性能稍好一些，而对于极度嘈杂的数据，我们的算法更准确（高于$ 20-40 \％$ $ $相对错误，这是在天文学领域中特别感兴趣的情况）。在这个范围内，通过我们的重建获得的残差的标准偏差可能比原始测量值低的数量级要高。重现本报告中介绍的所有结果所需的源代码，包括该方法的实现，请参见https://github.com/pablomsanala/fabada。
The aim of this paper is to describe a novel non-parametric noise reduction technique from the point of view of Bayesian inference that may automatically improve the signal-to-noise ratio of one- and two-dimensional data, such as e.g. astronomical images and spectra. The algorithm iteratively evaluates possible smoothed versions of the data, the smooth models, obtaining an estimation of the underlying signal that is statistically compatible with the noisy measurements. Iterations stop based on the evidence and the $χ^2$ statistic of the last smooth model, and we compute the expected value of the signal as a weighted average of the whole set of smooth models. In this paper, we explain the mathematical formalism and numerical implementation of the algorithm, and we evaluate its performance in terms of the peak signal to noise ratio, the structural similarity index, and the time payload, using a battery of real astronomical observations. Our Fully Adaptive Bayesian Algorithm for Data Analysis (FABADA) yields results that, without any parameter tuning, are comparable to standard image processing algorithms whose parameters have been optimized based on the true signal to be recovered, something that is impossible in a real application. State-of-the-art non-parametric methods, such as BM3D, offer slightly better performance at high signal-to-noise ratio, while our algorithm is significantly more accurate for extremely noisy data (higher than $20-40\%$ relative errors, a situation of particular interest in the field of astronomy). In this range, the standard deviation of the residuals obtained by our reconstruction may become more than an order of magnitude lower than that of the original measurements. The source code needed to reproduce all the results presented in this report, including the implementation of the method, is publicly available at https://github.com/PabloMSanAla/fabada
