基于多尺度去噪正则化和深度神经网络的相位恢复
Phase Retrieval Based on Multi-Scale Regularization by Denoising and Deep Neural Networks

相位恢复问题是恢复信号丢失或损坏的相位信息，以实现信号的准确分析、处理和重建。相位恢复在许多领域都有广泛的应用，例如通信系统、图像处理和计算机视觉、雷达和无线电频谱感知和生物医学工程等。然而，传统的相位恢复算法在噪声存在的情况下很难实现恢复任务。幸运的是，各种先进算法的不断提出和改进以及深度学习的兴起为处理相位恢复问题提供了很大的帮助。为了解决单个去噪正则项不能涵盖图像的全部先验信息的问题，本文考虑多尺度的去噪正则化求解带有噪声的相位恢复问题，它基于去噪正则化框架，而且它通过在优化问题中引入正则化项来实现去除图像中的噪声。为了解决将去噪正则化和FFDNet一起考虑求解带有噪声的相位恢复问题时恢复效果不好的问题，本文充分利用DnCNN和FFDNet这两种去噪器的优点，在相位恢复的过程中分情况使用这两种去噪器。最后本文通过数值实验表明了改进策略在视觉效果和量化数值上都有更加优异的表现。
Phase retrieval problem is to recover the lost or damaged phase information in order to realize the accurate analysis, processing and reconstruction of the signal. Phase retrieval is widely used in many fields, such as communication systems, image processing and computer vision, radar and radio spectrum sensing and biomedical engineering. However, the traditional phase retrieval algorithms are difficult to achieve the recovery task in the presence of noise. Fortunately, the continuous proposal and improvement of various advanced algorithms and the rise of deep learning provide great help to deal with the phase retrieval problem. In order to solve the problem that a single denoising regularization cannot cover all the prior information of the image, this paper considers multi-scale denoising regularizations to solve the phase retrieval problem disturbed by noise, which is based on the regularization by denoising framework and it removes the noise in the image by introducing a regularization term into the optimization problem. Additionally, in order to solve the problem of poor recovery effect when regularization by denoising and FFDNet are considered together to solve the phase retrieval contaminated with noise, this paper makes full use of the advantages of DnCNN and FFDNet, so these two kinds of denoising in different cases are combined to deal with the phase retrieval. Finally, numerical experiments show that the improved strategies have better performance in visual effect and quantitative value.