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。

基于白度的分层学习在图像中的正则化参数

Whiteness-based bilevel learning of regularization parameters in imaging

Deep Belief Networks which are hierarchical generative models are effective
tools for feature representation and extraction. Furthermore, DBNs can be used
in numerous aspects of Machine Learning such as image denoising. In this paper,
we propose a novel method for image denoising which relies on the DBNs' ability
in feature representation. This work is based upon learning of the noise
behavior. Generally, features which are extracted using DBNs are presented as
the values of the last layer nodes. We train a DBN a way that the network
totally distinguishes between nodes presenting noise and nodes presenting image
content in the last later of DBN, i.e. the nodes in the last layer of trained
DBN are divided into two distinct groups of nodes. After detecting the nodes
which are presenting the noise, we are able to make the noise nodes inactive
and reconstruct a noiseless image. In section 4 we explore the results of
applying this method on the MNIST dataset of handwritten digits which is
corrupted with additive white Gaussian noise (AWGN). A reduction of 65.9% in
average mean square error (MSE) was achieved when the proposed method was used
for the reconstruction of the noisy images.

本文提出了一种新的基于深度置信网络的图像去噪方法，在 MNIST 数据集上的应用结果显示，该方法在去噪方面取得了显著的成果。

用于图像去噪的深度信念网络

Deep Belief Networks for Image Denoising

New upper and lower bounds are presented on the capacity of the free-space
optical intensity channel. This channel is characterized by inputs that are
nonnegative (representing the transmitted optical intensity) and by outputs
that are corrupted by additive white Gaussian noise (because in free space the
disturbances arise from many independent sources). Due to battery and safety
reasons the inputs are simultaneously constrained in both their average and
peak power. For a fixed ratio of the average power to the peak power the
difference between the upper and the lower bounds tends to zero as the average
power tends to infinity, and the ratio of the upper and lower bounds tends to
one as the average power tends to zero. The case where only an average-power
constraint is imposed on the input is treated separately. In this case, the
difference of the upper and lower bound tends to 0 as the average power tends
to infinity, and their ratio tends to a constant as the power tends to zero.

本文提出了关于自由空间光强通道容量的新上下界，通道的输入为非负（代表传输光强），输出受大量独立源引起的加性白噪声影响，因电池和安全原因，输入同时受到平均功率和峰值功率的限制。