基于高阶信息和深度表示的图像复原研究

Image restoration is a typically ill-posed and inverse problem, which can be solved by changing into well-posed problem with the prior model. Among these image models, the regularization model, which is based on the distribution of one-order gradients or matrix spectrum, ignores the higher-order image property, while the shallow model, which is based on artificial neural network, cannot represent the deep image features. Therefore, exploring the higher-order prior model and the deep feature representation for image restoration becomes the hot spot in the current image restoration research field. This project aims to propose an image restoration algorithm combining high-order regularization and deep learning, and we will do research in “Higher-order information + Deep representation” image restoration from three aspects of the prior modeling, key technologies and typical examples for verification. First, study the information complementary mechanism between higher-order and deep image models and propose the unified framework based on these two kind of models, as the theoretical basis of the proposed algorithms. Secondly, study the following key technologies for image deblur, denoise and resolution enhancement: the adaptive regularization based on higher-order variation, the adaptive regularization based on the spectrum of higher-order tensor, and the prior learning of deep textures. Finally, verify the proposed theories and key technologies by the application in restoring the image degraded by the atmosphere turbulence. Through these researches above, to push the limits of the lower-order prior model and shallow feature representation, has great significance to satisfy the needs of image restoration theory and application development.

图像复原作为典型病态求逆问题，需要利用先验知识建模来转变为良态适定问题求解。现有图像模型中，基于一阶梯度或矩阵谱分布正则化的图像模型忽略图像高阶特性，而基于浅层人工神经网络的图像模型不能表示图像深层特征，探索图像高阶先验建模和深层特征表示在图像复原中的作用成为当前图像复原领域研究热点。本项目旨在提出一种结合高阶正则化和深度学习的图像复原算法，从先验模型、关键技术、实例验证三方面开展“高阶信息+深度表示”图像复原研究。首先，研究高阶和深度图像模型之间的信息互补机制及其复原统一框架，为所提算法提供理论与模型基础；其次，研究自适应高阶变分正则化、高阶张量自适应谱正则化与深度纹理先验学习关键技术，实现退化图像模糊和噪声去除以及分辨率增强；最后，进行大气湍流退化图像复原应用，验证提出的理论与关键技术。通过上述研究，突破图像低阶先验模型和浅层特征表示限制，对图像复原理论和应用具有重要意义。

图像复原作为典型病态求逆问题，需要利用先验知识建模来转变为良态适定问题求解。现有图像模型中，基于一阶梯度或矩阵谱分布正则化的图像模型忽略图像高阶特性，而基于浅层人工神经网络的图像模型不能表示图像深层特征，探索图像高阶先验建模和深层特征表示在图像复原中的作用成为当前图像复原领域研究热点。本课题实现了基于高阶信息和深度表示的图像复原的三个目标。首先，在理论方法创新方面，1）提出了基于扭转张量低秩模型的图像复原算法，2）提出了求解稀疏正则化约束的快速Bregman迭代复原算法并证明了其收敛性。其次，在关键技术突破方面，1）基于张量低秩和稀疏分解模型，提出视觉显著性驱动的运动目标检测算法，2）提出了基于稀疏正则化约束的多帧湍流图像畸变校正和基于形变场引导的时-空核回归多帧融合方法，3）基于张量低秩模型，提出非局部图像去噪算法。最后，在验证性应用方面，本课题的理论方法和关键技术均应用于国家某重大战略工程，成功服务于国防科学基础建设，并且在结题考核中获得了极高的评价。