论文标题
使用Poisson数据的预期最大化算法的预测风险估计
Predictive risk estimation for the Expectation Maximization algorithm with Poisson data
论文作者
论文摘要
在这项工作中，当损失函数是kullback-leibler差异时，我们引入了一个新颖的预测风险估计器，以定义一个正则化参数的选择规则，以实现期望最大化（EM）算法的选择规则。为了这个目的，我们证明了高斯变量的Stein引理的泊松对应物，从此结果，我们得出了拟议的估计器，显示出其类比，与众所周知的Stein无偏见的风险估计器有效期有效二次损失。我们证明，在正则化方法上的某些轻度条件下，所提出的估计量渐近地公正，测量计数的数量增加。我们表明，这些条件是通过EM算法满足的，然后我们将此估计值选择其最佳重建。在图像反卷积的情况下，我们提出了一些数值测试，将拟议估计量的性能与文献中可用的其他方法进行了比较，无论是在反犯罪和非犯罪情况下。
In this work, we introduce a novel estimator of the predictive risk with Poisson data, when the loss function is the Kullback-Leibler divergence, in order to define a regularization parameter's choice rule for the Expectation Maximization (EM) algorithm. To this aim, we prove a Poisson counterpart of the Stein's Lemma for Gaussian variables, and from this result we derive the proposed estimator showing its analogies with the well-known Stein's Unbiased Risk Estimator valid for a quadratic loss. We prove that the proposed estimator is asymptotically unbiased with increasing number of measured counts, under certain mild conditions on the regularization method. We show that these conditions are satisfied by the EM algorithm and then we apply this estimator to select its optimal reconstruction. We present some numerical tests in the case of image deconvolution, comparing the performances of the proposed estimator with other methods available in the literature, both in the inverse crime and non-inverse crime setting.
