In this paper, we propose inertial forward-backward splitting algorithm to approximate the solution of common variational inclusion problems. By using the inertial technique with parallel monotone hybrid methods we prove strong convergence results under some suitable conditions in Hilbert spaces. We then give some applications and numerical experiments for supporting our main results which shows that our proposed inertial hybrid method has better convergence rate than existing algorithms. Further, we apply our result to solve a common convex minimization problem and a common split feasibility problem. Finally, we use our proposed algorithm to solve the unconstrained image restoration problems and we can show that our algorithm is flexibility and good quality to use for common types of blur effects.

中文翻译：

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涉及惯性并行单调混合方法的常见变分包含问题的强收敛分析，用于图像恢复的新应用

在本文中，我们提出惯性前向后向分裂算法来逼近常见变分包含问题的解。通过使用惯性技术和并行单调混合方法，我们证明了在希尔伯特空间中某些合适条件下的强收敛结果。然后我们给出了一些应用和数值实验来支持我们的主要结果，这表明我们提出的惯性混合方法比现有算法具有更好的收敛速度。此外，我们将我们的结果应用于解决常见的凸最小化问题和常见的拆分可行性问题。最后，我们使用我们提出的算法来解决无约束图像恢复问题，我们可以证明我们的算法具有灵活性和良好的质量，可用于常见类型的模糊效果。