基于无训练神经网络和显式先验的非高斯噪声下图像恢复

图像中噪声和模糊不可避免，因此图像恢复成为理解图像至关重要的第一步。本项目中考虑的脉冲，泊松和乘性噪声不同于加性高斯噪声，一般很难去除，通常出现在光学成像系统中，并且大多带有模糊和其它类型噪声。神经网络在图像恢复方面已经取得了很大的成功，但是大多数依赖于对大量任务特定数据的训练。为了弥补这一缺陷并改进整体正则化效果，本项目将无训练神经网络和显式先验相结合，其中无训练神经网络可从网络体系结构中合成图像，此结构足以从单个图像中捕获足够的图像特征，因此避免使用训练数据集。为处理泊松和乘性噪声，本项目将定制损失函数并改进激活函数，同时替换网络的输入以便更好地和显式先验相结合。为了消除脉冲噪声，本项目将去噪问题变为修复问题，然后在框架中使用部分卷积以修复图像。然后结合多重结构光照模型，将该框架扩展用于处理相位恢复问题，从记录的受脉冲噪声和泊松噪声影响的衍射图像中重建目标物体的图像。

Because of unavoidable noise and blur in practice, image recovery becomes the first vital step towards understanding the image. In this proposal, we focus on impulse noise, Poisson noise and multiplicative noise which are different from additive Gaussian noise, and difficult to remove. Non-Gaussian noise is commonly found in optical imaging systems, and most times it comes with blur and Gaussian noise. Neural networks have achieved great success in image restoration, but most of them rely on the training step that requires large amounts of task-specific training data. To remedy this drawback and enrich the overall regularization effect, we join force of the untrained neural network and the explicit prior, the untrained neural network can synthesize the recovered image from a given network architecture. This network is sufficient to capture enough image features from a single image, therefore avoiding the demand of training data sets. To deal with Poisson noise and multiplicative noise, we customize the loss function, improve the activation function and also change the input of the network to better work with the explicit prior. For removal of impulse noise, we first turn the denoising problem into an inpainting problem, then we equip the framework with the partial convolution to restore the polluted image. The framework then be extended to deal with phase retrieval problems, it combines multiple structured illuminations to reconstruct the image of the targeting object from the recorded diffraction pattern which suffers from impulse noise and Poisson noise.