This thesis analyzes the challenging problem of Image Deblurring based on classical theorems and state-of-art methods proposed in recent years. By spectral analysis we mathematically show the effective of spectral regularization methods, and point out the linking between the spectral filtering result and the solution of the regularization optimization objective. For ill-posed problems like image deblurring, the optimization objective contains a regularization term (also called the regularization functional) that encodes our prior knowledge into the solution. We demonstrate how to craft a regularization term by hand using the idea of maximum a posterior estimation. Then, we point out the limitations of such regularization-based methods, and step into the neural-network based methods. Based on the idea of Wasserstein generative adversarial models, we can train a CNN to learn the regularization functional. Such data-driven approaches are able to capture the complexity, which may not be analytically modellable. Besides, in recent years with the improvement of architectures, the network has been able to output an image closely approximating the ground truth given the blurry observation. The Generative Adversarial Network (GAN) works on this Image-to-Image translation idea. We analyze the DeblurGAN-v2 method proposed by Orest Kupyn et al. [14] in 2019 based on numerical tests. And, based on the experimental results and our knowledge, we put forward some suggestions for improvement on this method.
翻译:这篇论文分析了基于古典理论和近年提出的最先进方法的图像Deblurring挑战性问题。 通过光谱分析, 我们数学地展示了光谱正规化方法的有效性, 并指出了光谱过滤结果与正规化优化目标解决方案之间的联系。 对于像图像模糊这样的错误问题, 优化目标包含一个正规化术语( 也称为正规化功能 ), 将我们先前的知识编码到解决方案中。 我们展示了如何用手来设计一个正规化术语。 我们演示了如何使用最高事后估计理念来亲手设计一个正规化术语。 然后, 我们用光谱分析方法指出这些基于常规的方法的局限性, 并进入基于神经网络的方法。 根据瓦塞斯特斯坦基因对抗性对抗模型的想法, 我们可以训练CNN来学习正规化功能。 这种数据驱动方法可以捕捉复杂性, 而这些复杂性也许不是分析模型。 此外, 近年来, 网络能够通过模糊的观察, 能够输出一个非常接近地面真相的图像。 我们用GAdversari2 和SDBA-A-A-A-A-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-