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出各分量信号，若仅需关注特定信号的特定属性，则可能带来不必要的计算复杂性。本研究针对简化的"统计分量分离"问题，旨在从含噪混合信号中恢复目标信号的一组预定义统计描述量。在假设可获取噪声过程样本的条件下，我们提出了一种通过匹配含噪候选解与观测混合信号统计特征的方法。首先通过可解析计算的基础案例验证该方法的行为特性，随后将其应用于图像去噪场景：1）基于小波变换的描述符；2）基于卷积神经网络的描述符（在天体物理与ImageNet数据集上）。研究结果表明，对于情况1），该方法在多数场景下能比标准去噪方法更准确地恢复目标数据统计描述量。值得注意的是，尽管该方法并非为全信号重建而设计，其在峰值信噪比指标上仍表现优异。相比之下，表征方法2）对图像去噪的适用性较弱。最后，我们引入扩散逐步算法对该方法进行扩展，该算法为初始方法提供了新视角，并在特定条件下展现出图像去噪领域的应用潜力。