Variational regularization, renowned for its sound theoretical foundations and impressive performance, is widely used in image restoration. The traditional regularization models typically use a predefined regularizer to promote smoothness in the solution. However, these models do not explicitly take into account any external information that should be preserved in the restoration. In this paper, we introduce a novel guided regularization model to enhance the efficacy of traditional regularization. Our model incorporates an external guidance regularizer, utilizing a guidance image to bolster the quality of restoration. By integrating this external information into the regularization process, the model is better equipped to preserve specific features or attributes indicated by the guidance image, leading to more accurate and aesthetically pleasing restored images. Furthermore, we demonstrate the convexity of the model and prove the existence and uniqueness of the solution. The alternating direction method of multipliers (ADMM) algorithm is employed to numerically solve the proposed model. In the experimental evaluation, the proposed model is applied to image denoising and deblurring tasks. The experiments successfully validate the proposed model and algorithm. Compared with several state-of-the-art models, the proposed model demonstrates the best performance in terms of peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM).

中文翻译：

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引导正则化及其在图像恢复中的应用


变分正则化以其扎实的理论基础和令人印象深刻的性能而闻名，广泛应用于图像恢复。传统的正则化模型通常使用预定义的正则化器来提高解决方案的平滑度。然而，这些模型没有明确考虑修复中应保留的任何外部信息。在本文中，我们引入了一种新颖的引导正则化模型来增强传统正则化的功效。我们的模型结合了外部引导正则器，利用引导图像来提高恢复质量。通过将这些外部信息集成到正则化过程中，模型可以更好地保留引导图像指示的特定特征或属性，从而获得更准确且美观的恢复图像。此外，我们证明了模型的凸性并证明了解的存在性和唯一性。采用交替方向乘子法（ADMM）算法对所提出的模型进行数值求解。在实验评估中，所提出的模型应用于图像去噪和去模糊任务。实验成功验证了所提出的模型和算法。与几种最先进的模型相比，所提出的模型在峰值信噪比（PSNR）和结构相似指数（SSIM）方面表现出最佳性能。