Tweedie distributions are a special case of exponential dispersion models, which are often used in classical statistics as distributions for generalized linear models. Here, we reveal that Tweedie distributions also play key roles in modern deep learning era, leading to a distribution independent self-supervised image denoising formula without clean reference images. Specifically, by combining with the recent Noise2Score self-supervised image denoising approach and the saddle point approximation of Tweedie distribution, we can provide a general closed-form denoising formula that can be used for large classes of noise distributions without ever knowing the underlying noise distribution. Similar to the original Noise2Score, the new approach is composed of two successive steps: score matching using perturbed noisy images, followed by a closed form image denoising formula via distribution-independent Tweedie's formula. This also suggests a systematic algorithm to estimate the noise model and noise parameters for a given noisy image data set. Through extensive experiments, we demonstrate that the proposed method can accurately estimate noise models and parameters, and provide the state-of-the-art self-supervised image denoising performance in the benchmark dataset and real-world dataset.
翻译:Tweedie 分布是指数分散模型的一个特例, 古典统计中通常使用这种模型作为通用线性模型的分布。 在这里, 我们发现Tweedie 分布在现代深层学习时代也发挥着关键作用, 导致一个独立分布的自监督图像除尘公式, 没有干净的参考图像。 具体来说, 与最近的Noise2Scent 自我监督的图像脱色方法和Tweedie分布的马鞍点近似值相结合, 我们可以提供一种一般的封闭式脱色公式, 可用于大型噪音分布类别, 而根本不知道潜在的噪音分布。 与原始的Noise2Score相似, 新的方法由两个连续步骤组成: 使用周遭噪音图像进行比对等, 之后是封闭形式图像通过分布独立 Tweedie 的公式进行脱色公式。 这还表明一种系统的算法, 用来估计噪音模型和噪音参数, 用于给定的噪音图像数据集。 通过广泛的实验, 我们证明拟议的方法可以准确估计噪音模型和参数, 并提供最先进的自我监督的图像基准数据。