Poisson image deblurring, which aims to restore the latent image from its blurred and noisy observation, has drawn significant attention in image processing. Due to its ill-posed nature, enhancing image quality often involves incorporating a well-defined prior to effectively regularize the ill-posed inverse problem. Building upon the framelet system, we propose a frame-based nonconvex regularization method for Poisson image deblurring. The method is formulated by combining a data-fitting term with the difference of two norms, namely and , on the latent image. We solve the optimization problem by combining the difference of convex functions algorithm (DCA) with the alternating direction method of multipliers (ADMM), establishing its convergence. We further employ a simulated annealing procedure and show that proposed algorithm almost certainly converges to a global minimum. Two different approaches are employed to handle the frame-based norm within the ADMM framework. In particular, the frame-based nonconvex regularization method is also considered for the blind Poisson problem. An effective recovery model and its algorithm are presented. Experimental results demonstrate the effectiveness of our proposed models compared with other models in terms of quantitative metrics and visual quality.

中文翻译：

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使用基于帧的非凸正则化进行泊松图像去模糊

泊松图像去模糊旨在从模糊和噪声的观察中恢复潜像，在图像处理中引起了广泛的关注。由于其不适定性质，增强图像质量通常需要结合明确定义的先验，以有效地规范不适定逆问题。在小框架系统的基础上，我们提出了一种基于框架的非凸正则化泊松图像去模糊方法。该方法是通过将数据拟合项与潜像上的两个范数（即 和 ）的差异相结合来制定的。我们通过将凸函数差分算法（DCA）与乘子交替方向法（ADMM）相结合来解决优化问题，建立其收敛性。我们进一步采用模拟退火程序，并表明所提出的算法几乎肯定会收敛到全局最小值。采用两种不同的方法来处理 ADMM 框架内基于框架的规范。特别地，针对盲泊松问题还考虑了基于框架的非凸正则化方法。提出了一种有效的恢复模型及其算法。实验结果证明了我们提出的模型在定量指标和视觉质量方面与其他模型相比的有效性。