Empirical Bayes Poisson matrix completion
针对泊松矩阵去噪和补全问题，提出经验贝叶斯方法EBPM算法，无需调参且优于核范数惩罚方法，适用于图像处理等实际数据。
An empirical Bayes method for the Poisson matrix denoising and completion problems is proposed, and a corresponding algorithm called EBPM (Empirical Bayes Poisson Matrix) is developed. This approach is motivated by the non-central singular value shrinkage prior, which was used for the estimation of the mean matrix parameter of a matrix-variate normal distribution . Numerical experiments show that the EBPM algorithm outperforms the common nuclear norm penalized method in both matrix denoising and completion. The EBPM algorithm is highly efficient and does not require heuristic parameter tuning, as opposed to the nuclear norm penalized method, in which the regularization parameter should be selected. The EBPM algorithm also performs better than others in real-data applications.