论文标题
在泊松噪声下图像修复中TGV正常化程序的自动参数选择
Automatic parameter selection for the TGV regularizer in image restoration under Poisson noise
论文作者
论文摘要
我们解决了泊松噪声腐败下的图像恢复问题。在这种情况下，kullback-leibler差异通常在变化框架中作为数据保真度项，与二阶总体广义变化（TGV $^2 $）相结合。众所周知，TGV $^2 $正规器能够在图像中保留平滑和零件的常数特征，但是其行为会受到其表达式出现的参数的合适设置。我们提出了一个层次的贝叶斯公式，对原始问题的均匀公式以及最大的后验估计方法，根据该方法，可以通过最小化给定的成本功能来共同估算未知的图像和参数。最小化问题是通过基于乘数交替方向方法的方案解决的，该方案还结合了通过流行的差异原理自动选择正则化参数的过程。计算结果表明我们的提案有效性。
We address the image restoration problem under Poisson noise corruption. The Kullback-Leibler divergence, which is typically adopted in the variational framework as data fidelity term in this case, is coupled with the second-order Total Generalized Variation (TGV$^2$). The TGV$^2$ regularizer is known to be capable of preserving both smooth and piece-wise constant features in the image, however its behavior is subject to a suitable setting of the parameters arising in its expression. We propose a hierarchical Bayesian formulation of the original problem coupled with a Maximum A Posteriori estimation approach, according to which the unknown image and parameters can be jointly and automatically estimated by minimizing a given cost functional. The minimization problem is tackled via a scheme based on the Alternating Direction Method of Multipliers, which also incorporates a procedure for the automatic selection of the regularization parameter by means of a popular discrepancy principle. Computational results show the effectiveness of our proposal.
