Abstract
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.
Abstract (translated)
图像平滑是一种基本的图像处理操作，它保留了底层结构（如强边缘和轮廓），同时移除图像中的小细节和纹理。许多图像平滑算法依赖于计算局部窗口统计信息或求解优化问题。最近最先进的方法利用深度学习技术，但它们需要精心准备的训练数据集。由于为图像平滑构建合适的训练数据集颇具挑战性，我们提出了一种名为DIP-$\ell_0$（Deep Image Prior）的框架，并在该框架中引入了$\ell_0$梯度正则化器。这个框架能够在无需任何训练数据的情况下实现高质量的图像平滑。 为了有效最小化含有非凸且不光滑的$\ell_0$“范数”的相关损失函数，我们开发了一种交替方向乘子法算法，并利用现成的$\ell_0$梯度最小化求解器。数值实验表明，所提出的DIP-$\ell_0$框架在边缘保护型图像平滑和JPEG伪影去除方面优于许多其他图像平滑算法。
URL
https://arxiv.org/abs/2601.13400
