We propose a general framework for denoising high-dimensional measurements
which requires no prior on the signal, no estimate of the noise, and no clean
training data. The only assumption is that the noise exhibits statistical
independence across different dimensions of the measurement, while the true
signal exhibits some correlation. For a broad class of functions
("$\mathcal{J}$-invariant"), it is then possible to estimate the performance of
a denoiser from noisy data alone. This allows us to calibrate
$\mathcal{J}$-invariant versions of any parameterised denoising algorithm, from
the single hyperparameter of a median filter to the millions of weights of a
deep neural network. We demonstrate this on natural image and microscopy data,
where we exploit noise independence between pixels, and on single-cell gene
expression data, where we exploit independence between detections of individual
molecules. This framework generalizes recent work on training neural nets from
noisy images and on cross-validation for matrix factorization.

提出了一种通用框架，用于去噪高维度测量，不需要先验信号、噪声估计和干净数据训练，仅假设噪声在不同维度上具有统计独立性，真实信号呈现某种相关性。