发表机构
University of Mohaghegh Ardabili（莫哈格·阿尔达比勒大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对泊松噪声下的图像去模糊问题，提出使用极小极大凹惩罚和加权 $\ell_1$ 正则化的非盲与盲方法，基于ADMM求解非凸模型，实验验证其有效性。
AI 中文摘要
图像是各种科学中的重要工具。尽管拍照工具不断发展，但在实践中创建清晰且无噪声的图像仍然具有挑战性。特别是，泊松噪声影响医学和天文图像，并降低其质量。此外，模糊是影响图像质量的另一个因素。当我们对点扩散函数（PSF）没有信息时，图像恢复问题变得非常复杂。这类问题被称为盲问题。然而，在某些图像中，例如一些天文图像，PSF的类型可以被指定，这类问题被称为非盲问题。全变分（TV）是解决此类逆问题的广泛使用的方法，其中惩罚函数的选择是影响方法性能的最关键因素。在本文中，为了提高边缘保持，我们采用了分数阶导数的加权 $\ell_1$ 正则化。此外，我们提出了一种在泊松噪声下的非盲和盲图像去模糊方法，使用极小极大凹惩罚（MCP），这是一种连续的、促进稀疏性的且几乎无偏的正则化器。该公式导致一个非凸优化模型。为了解决所提出的模型，我们引入了一种基于交替方向乘子法（ADMM）的高效数值算法，并对其收敛性进行了分析。最后，通过在多种图像上的广泛实验证明了所提出算法的有效性。
英文摘要
Images are important tools in various sciences. Despite the development of photo-taking tools, creating clear and image without noise remains challenging in practice. In particular, Poisson noise has an effect on medical and astronomical images, and reduces their quality. Additionally, blur is another factor that has an effect on image quality. The problem of image restoration becomes very complicated when we have no information about the Point Spread Function (PSF). These types of problems are known as blind case. However, in some images, such as some astronomical images, the type of PSF can be specified, and these types of problems are known as nonblind problems. Total Variation (TV) is a widely used method for solving such inverse problems, where the selection of the penalty function is the most critical factor that affects the method's performance. In this paper, to improve edge preservation, we employ a reweighted $\ell_1$-regularization of the fractional order derivative. Furthermore, we propose a nonblind and blind image deblurring approach under Poisson noise using the Minimax Concave Penalty (MCP), which is a continuous, sparsity promoting, and nearly unbiased regularizer. This formulation leads to a nonconvex optimization model. To solve the proposed model, we introduce an efficient numerical algorithm based on the Alternating Direction Method of Multipliers (ADMM) and provide an analysis of its convergence. Finally, the effectiveness of the proposed algorithm are demonstrated through extensive experiments on various images.
