The total variation (TV) method is an image denoising technique that aims to reduce noise by minimizing the total variation of the image, which measures the variation in pixel intensities. The TV method has been widely applied in image processing and computer vision for its ability to preserve edges and enhance image quality. In this paper, we propose an improved TV model for image denoising and the associated numerical algorithm to carry out the procedure, which is particularly effective in removing several types of noises and their combinations. Our improved model admits a unique solution and the associated numerical algorithm guarantees the convergence. Numerical experiments are demonstrated to show improved effectiveness and denoising quality compared to other TV models. Such encouraging results further enhance the utility of the TV method in image processing.

翻译：全变分（TV）方法是一种通过最小化图像全变分（即像素强度变化量）来降低噪声的图像去噪技术。该方法因其能够保持边缘并提升图像质量，在图像处理和计算机视觉领域得到了广泛应用。本文提出了一种改进的TV模型用于图像去噪，并给出了相应的数值算法来执行该过程，该模型在去除多种类型噪声及其组合方面尤为有效。我们改进的模型具有唯一解，且相应的数值算法保证了收敛性。数值实验表明，与其他TV模型相比，本文方法在去噪效果和质量上均有提升。这些令人鼓舞的结果进一步增强了TV方法在图像处理中的实用性。