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：从加性混合中分离信号，当仅关注特定信号的特定性质时，可能是一个不必要复杂的问题。在本研究中，我们探讨更简单的“统计分量分离”问题，其目标是从噪声混合中恢复目标信号的预定义统计描述符。假设可获取噪声过程的样本，我们研究了一种方法，该方法旨在使受噪声样本污染的候选解统计量与观测混合的统计量相匹配。首先，通过具有解析可算性的简单示例分析该方法的行为。随后，将其应用于图像去噪场景，分别采用：1）基于小波的描述符；2）基于卷积神经网络（ConvNet）的描述符，在天体物理学和ImageNet数据上进行实验。在情况1）中，我们表明该方法在大多数情况下比标准去噪方法能更好地恢复目标数据的描述符。此外，尽管非为此目的而设计，该方法在全信号重建的峰值信噪比（PSNR）方面表现异常出色。相比之下，表示方式2）似乎不太适合图像去噪。最后，我们通过引入一种扩散步进算法对该方法进行扩展，该算法为初始方法提供了新视角，并在特定条件下为图像去噪带来了有前景的结果。