Owing to its significant success, the prior imposed on gradient maps has consistently been a subject of great interest in the field of image processing. Total variation (TV), one of the most representative regularizers, is known for its ability to capture the sparsity of gradient maps. Nonetheless, TV and its variants often underestimate the gradient maps, leading to the weakening of edges and details whose gradients should not be zero in the original image. Recently, total deep variation (TDV) has been introduced, assuming the sparsity of feature maps, which provides a flexible regularization learned from large-scale datasets for a specific task. However, TDV requires retraining when the image or task changes, limiting its versatility. In this paper, we propose a neural gradient regularizer (NGR) that expresses the gradient map as the output of a neural network. Unlike existing methods, NGR does not rely on the sparsity assumption, thereby avoiding the underestimation of gradient maps. NGR is applicable to various image types and different image processing tasks, functioning in a zero-shot learning fashion, making it a versatile and plug-and-play regularizer. Extensive experimental results demonstrate the superior performance of NGR over state-of-the-art counterparts for a range of different tasks, further validating its effectiveness and versatility.

翻译：由于其显著的成功，对梯度图施加的先验在图像处理领域一直备受关注。总变分（TV）作为最具代表性的正则化器之一，以其捕捉梯度图稀疏性的能力而闻名。然而，TV及其变体常常低估梯度图，导致原始图像中梯度不应为零的边缘和细节被削弱。近年来，总深度变分（TDV）被引入，其假设特征图具有稀疏性，为特定任务提供了从大规模数据集中学习到的灵活正则化。但TDV在图像或任务发生变化时需要重新训练，限制了其通用性。本文提出一种神经梯度正则化器（NGR），将梯度图表示为神经网络的输出。与现有方法不同，NGR不依赖稀疏性假设，从而避免了对梯度图的低估。NGR适用于多种图像类型和不同的图像处理任务，以零样本学习方式运行，成为一种通用且即插即用的正则化器。大量实验结果表明，NGR在一系列不同任务中的性能优于最先进的同类方法，进一步验证了其有效性和通用性。