图对信息分析中的张量算子学习问题

Information processing of image pairs focus on the problem of developing the maps between the images, and it is useful in kinds of learning-based image processing problems. For further research on the issue, two core scientific topics, including the learnability and the generalization of the information of the image pairs are considered in this research project. The learnability emphasizes on the research of the mathematic methods to model the information of the image pairs and the feasibility of developing learning algorithms. The generalization emphasizes on the research of the applications and the convergence of these algorithms in various image processing tasks. To address both of the key topics, the novel results on tensor operators and the supervised/semi-supervised learning theory are employed to research the problems of designing the learning-based algorithms and their convergence within the setting of tensor-value regression. Specific research contains the problems of designing the supervised/semi-supervised tensor-value regression algorithms, the applications of these algorithms in the super-resolution and the image denoising, the convergence and the rate of convergence of these algorithms. The smooth implementation of the project could enrich the research of machine learning and the learning theory, and promote technical progress of the learning-based image processing. Therefore, the project is significant in the field of machine learning, learning theory, and image processing.

图对信息处理问题以图像间映射关系为主要研究对象，是学习型图像处理技术研究中的重要共性问题。为深入探讨该问题，本项目拟围绕图对信息的可学习性及可推广性两个关键科学问题开展研究。可学习性问题侧重研究图对信息模型化的数学方法及算法可行性。可推广性问题侧重研究图对信息模型的实用效果及算法收敛性分析。针对上述关键科学问题，本项目拟以张量算子研究的新成果为数学基础，以监督/半监督学习理论为指导，在张量值回归模型下研究图对信息学习的算法设计、应用及收敛性问题。具体研究内容包含：监督/半监督张量值回归算法的设计问题；监督/半监督张量值回归算法在超分辨率及图像降噪中的应用；监督/半监督张量值回归算法的收敛性及收敛阶讨论。本项研究的顺利开展将丰富机器学习及学习理论的研究内容，推动学习型图像技术的发展。因此，本项研究理论意义重要，应用前景广泛，具有较高研究价值。

课题组围绕图对信息的表示、提取及应用问题开展了图像质量提升、目标识别及元学习算法设计及分析等三方面的研究工作。课题组借鉴胶囊网络的设计经验，提出了一类基于胶囊网络的图对信息表示、提取及应用方法。基于该方法，设计了适用于图像质量改善问题的回归型算法；以及适用于目标识别及元学习问题的分类型算法。两类算法在适用问题中均取得了良好的测试性能。其中，图像质量改善算法被应用于少数民族古文字处理问题中；分类算法被应用于遥感目标识别及少样本元学习问题中。实测结果显示，图对信息的应用较为明显的提升了上述算法的应用效果。基于上述工作，课题组发表了10篇学术论文，取得了2件软件著作权，获得了1项云南省自然科学奖。