标题： Richardson-Lucy去卷积与均方误差优化的数据展开的比较分析 显示英文标题

标题： Comparative Analysis of Richardson-Lucy Deconvolution and Data Unfolding with Mean Integrated Square Error Optimization

摘要： 基于最大似然的两种展开或反卷积算法被考虑：Richardson-Lucy方法和带有均方误差（MISE）优化的数据展开方法[10]。 展开被视为一种估计未知概率密度函数的过程。 可以应用外部和内部质量评估方法来实现这一目的。 在某些情况下，存在外部标准来评估反卷积的质量。 一个典型的例子是模糊图像的反卷积，其中恢复图像的清晰度作为质量的指标。 然而，定义这样的外部标准可能具有挑战性，尤其是在之前没有进行过测量的情况下。 在这些情况下，需要内部标准来独立于外部信息评估结果的质量。 本文讨论了两种内部标准：展开分布的MISE和展开分布相关矩阵的条件数。 这些内部质量标准被应用于使用相同数值数据对两种方法的比较分析。 分析结果表明，带有MISE优化的数据展开方法优于Richardson-Lucy方法。 显示英文摘要

摘要： Two maximum likelihood-based algorithms for unfolding or deconvolution are considered: the Richardson-Lucy method and the Data Unfolding method with Mean Integrated Square Error (MISE) optimization [10]. Unfolding is viewed as a procedure for estimating an unknown probability density function. Both external and internal quality assessment methods can be applied for this purpose. In some cases, external criteria exist to evaluate deconvolution quality. A typical example is the deconvolution of a blurred image, where the sharpness of the restored image serves as an indicator of quality. However, defining such external criteria can be challenging, particularly when a measurement has not been performed previously. In such instances, internal criteria are necessary to assess the quality of the result independently of external information. The article discusses two internal criteria: MISE for the unfolded distribution and the condition number of the correlation matrix of the unfolded distribution. These internal quality criteria are applied to a comparative analysis of the two methods using identical numerical data. The results of the analysis demonstrate the superiority of the Data Unfolding method with MISE optimization over the Richardson-Lucy method.