We consider an unsupervised bilevel optimization strategy for learning
regularization parameters in the context of imaging inverse problems in the
presence of additive white Gaussian noise. Compared to supervised and
semi-supervised metrics relying either on the prior knowledge of reference data
and/or on some (partial) knowledge on the noise statistics, the proposed
approach optimizes the whiteness of the residual between the observed data and
the observation model with no need of ground-truth data.We validate the
approach on standard Total Variation-regularized image deconvolution problems
which show that the proposed quality metric provides estimates close to the
mean-square error oracle and to discrepancy-based principles.

无监督双层优化策略可用于在成像反问题中学习正则化参数，解决加性白高斯噪声存在的问题。与依赖参考数据的监督和半监督度量以及依赖噪声统计的部分知识的方法相比，该方法无需地面真实数据，通过优化观测数据和观测模型之间残差的白化程度。我们在标准的总变差正则化图像去卷积问题上验证了该方法，结果表明提出的质量度量估计接近于均方误差和差异性原则。