Image smoothing is a fundamental image processing operation that preserves the underlying structure, such as strong edges and contours, and removes minor details and textures in an image. Many image smoothing algorithms rely on computing local window statistics or solving an optimization problem. Recent state-of-the-art methods leverage deep learning, but they require a carefully curated training dataset. Because constructing a proper training dataset for image smoothing is challenging, we propose DIP-$\ell_0$, a deep image prior framework that incorporates the $\ell_0$ gradient regularizer. This framework can perform high-quality image smoothing without any training data. To properly minimize the associated loss function that has the nonconvex, nonsmooth $\ell_0$ ``norm", we develop an alternating direction method of multipliers algorithm that utilizes an off-the-shelf $\ell_0$ gradient minimization solver. Numerical experiments demonstrate that the proposed DIP-$\ell_0$ outperforms many image smoothing algorithms in edge-preserving image smoothing and JPEG artifact removal.

翻译：图像平滑是一种基础的图像处理操作，其目的是在保留图像底层结构（如显著边缘与轮廓）的同时去除图像中的细微细节与纹理。许多图像平滑算法依赖于计算局部窗口统计量或求解优化问题。当前最先进的方法利用深度学习技术，但需要精心构建训练数据集。由于为图像平滑构建合适的训练数据集具有挑战性，我们提出DIP-$\ell_0$——一种融合了$\ell_0$梯度正则化的深度图像先验框架。该框架无需任何训练数据即可实现高质量的图像平滑。为有效最小化包含非凸、非光滑$\ell_0$“范数”的损失函数，我们开发了一种基于现成$\ell_0$梯度最小化求解器的交替方向乘子算法。数值实验表明，所提出的DIP-$\ell_0$在边缘保持图像平滑与JPEG伪影去除任务中优于多种图像平滑算法。