Separating signals from an additive mixture may be an unnecessarily hard problem when one is only interested in specific properties of a given signal. In this work, we tackle simpler "statistical component separation" problems that focus on recovering a predefined set of statistical descriptors of a target signal from a noisy mixture. Assuming access to samples of the noise process, we investigate a method devised to match the statistics of the solution candidate corrupted by noise samples with those of the observed mixture. We first analyze the behavior of this method using simple examples with analytically tractable calculations. Then, we apply it in an image denoising context employing 1) wavelet-based descriptors, 2) ConvNet-based descriptors on astrophysics and ImageNet data. In the case of 1), we show that our method better recovers the descriptors of the target data than a standard denoising method in most situations. Additionally, despite not constructed for this purpose, it performs surprisingly well in terms of peak signal-to-noise ratio on full signal reconstruction. In comparison, representation 2) appears less suitable for image denoising. Finally, we extend this method by introducing a diffusive stepwise algorithm which gives a new perspective to the initial method and leads to promising results for image denoising under specific circumstances.

翻译：从加性混合信号中分离信号可能是一个不必要的困难问题——当研究者仅关注某一信号的特定属性时尤为如此。本文针对简化的"统计分量分离"问题展开研究，其核心目标是从含噪混合信号中恢复目标信号的预定义统计描述子。在能够获取噪声过程样本的前提下，我们探索了一种方法：通过匹配经噪声样本污染的候选解统计量与观测混合信号统计量来实现恢复。首先利用可解析计算的简单示例分析该方法的行为模式，随后将其应用于图像去噪场景：1）基于小波的描述子；2）基于卷积神经网络的描述子（分别在天体物理数据与ImageNet数据上测试）。针对方案1），我们证明该方法在大多数情况下能比传统去噪方法更有效地恢复目标数据的描述子。此外，尽管该方法并非为全信号重构设计，其在峰值信噪比指标上仍展现出惊人效果。相较而言，方案2）在图像去噪中的适用性较弱。最后，我们通过引入扩散式逐步算法对该方法进行拓展，该算法为原始方法提供了全新视角，并在特定条件下为图像去噪带来具有前景的结果。