Image restoration, which aims to recover high-quality images from their corrupted counterparts, often faces the challenge of being an ill-posed problem that allows multiple solutions for a single input. However, most deep learning based works simply employ l1 loss to train their network in a deterministic way, resulting in over-smoothed predictions with inferior perceptual quality. In this work, we propose a novel method that shifts the focus from a deterministic pixel-by-pixel comparison to a statistical perspective, emphasizing the learning of distributions rather than individual pixel values. The core idea is to introduce spatial entropy into the loss function to measure the distribution difference between predictions and targets. To make this spatial entropy differentiable, we employ kernel density estimation (KDE) to approximate the probabilities for specific intensity values of each pixel with their neighbor areas. Specifically, we equip the entropy with diffusion models and aim for superior accuracy and enhanced perceptual quality over l1 based noise matching loss. In the experiments, we evaluate the proposed method for low light enhancement on two datasets and the NTIRE challenge 2024. All these results illustrate the effectiveness of our statistic-based entropy loss. Code is available at https://github.com/shermanlian/spatial-entropy-loss.

翻译：图像复原旨在从受损图像中恢复高质量图像，但常面临一个挑战：该问题本质上是不适定的，单个输入可能对应多个可行解。然而，大多数基于深度学习的方案仅采用L1损失以确定性方式训练网络，导致预测结果过度平滑，感知质量较差。本文提出一种新颖方法，将焦点从确定性逐像素比较转向统计视角，强调对分布的学习而非单个像素值。核心思想是将空间熵引入损失函数，用以衡量预测值与目标值之间的分布差异。为使该空间熵可微，我们采用核密度估计（KDE）来近似每个像素在其邻域内特定强度值的概率。具体而言，我们将熵与扩散模型结合，旨在比基于L1的噪声匹配损失实现更优的准确性和增强的感知质量。实验中，我们在两个数据集及NTIRE 2024挑战赛上评估了所提方法用于低光增强的效果。所有结果均证明了基于统计的熵损失的有效性。代码开源于https://github.com/shermanlian/spatial-entropy-loss。