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 intrinsic sparsity prior underlying 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 (i.e., image structures is not describable by sparse priors of gradient maps). 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 to retrain the network with image/task variations, limiting its versatility. To alleviate this issue, 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 any subjective sparsity or other prior assumptions on image gradient maps, 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：[translated abstract in Chinese] 由于其显著的成功，梯度图上的先验在图像处理领域一直备受关注。全变分（TV）作为最具代表性的正则化器之一，以其能够捕捉梯度图下固有的稀疏先验而闻名。然而，TV及其变体常常低估梯度图，导致边缘和细节（其梯度在原始图像中不应为零，即图像结构无法通过梯度图的稀疏先验描述）被弱化。最近，提出了一种总深度变分（TDV），它假设特征图具有稀疏性，为特定任务从大规模数据集中学习到一种灵活的正则化。然而，TDV需要根据图像/任务变化重新训练网络，限制了其通用性。为解决此问题，本文提出了一种神经梯度正则化器（NGR），它将梯度图表示为神经网络的输出。与现有方法不同，NGR不依赖于任何主观的稀疏性或图像梯度图上的其他先验假设，从而避免了梯度图的低估。NGR适用于各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在一系列不同任务上性能优于最先进的对比方法，进一步验证了其有效性和通用性。