基于分数阶Jacobian张量正则模型的图像修复方法研究

修复受损的航天或卫星影像对航天航空产业的发展具有巨大的支撑和促进作用。当前解决方案仍存在对复杂细节及弱结构特征修复精细度不高的问题。以多组份图像为研究对象，针对高频细节难检测处理、难兼顾噪声鲁棒性和难生成问题，提出分数阶Jacobian张量正则(FJTR)模型及其约束的修复新方法。为了有效处理细粒度特征，并解决与噪声鲁棒性相互制约的瓶颈问题，提出Jacobian扩展的分数阶结构张量以指导各向异性正则，从而构建线性凸的FJTR模型。在此基础上，为了耦合组份间局部特征相关性以指导空间正则，提出FJTR自适应加权正则的张量修复方法，提高复杂细节修复性能和混合噪声移除能力；针对深度网络难以生成精细细节及结构的问题，提出FJTR正则约束的多尺度语义修复方法，提高预测内容与上下文细节特征的正则一致性以及修复对象的分辨率。本项目研究成果对航天航空图像的精细复原具有革命性突破，具有重要学术价值和应用前景。

The restoration of damaged space or satellite imagery plays a significant role in supporting and promoting the development of aerospace industry. The current solution still has the problem of insufficient fineness of inpainting complex image details and weak structures. Aiming at solving the problem that high-frequency details are difficult to detect, guarantee noise robustness and generate, we put forward a fractional-order Jacobian tensor regularization (FJTR) model and two novel image inpainting methods constrained by the proposed model for multi-component image. In order to effectively tackle the fine-grained structures and solve the bottleneck problem of its mutually interacting with noise robustness, we put forward a fractional structure tensor expanded by Jacobian to guide the anisotropic regularization process, and accordingly build a linear and convex FJTR model. On this basis, in order to couple the correlation of local structural features between the different components to conduct spacial regularization, we propose a new adaptive weighted FJTR-in-space based tensor completion method, to improve the performance of recovery of complex details and removal of mixed noise; Aiming at solving the problem that deep learning networks have trouble in generating high-frequency details and fine structures, we propose a new FJTR-controlled multi-scale semantic restoration method, to retain the regularization consistency of fine features between the predicted content and the context and improve the resolution of the image to be fixed. The research results of this project have a revolutionary breakthrough in the fine restoration of aerospace images, which has important academic value and application prospect.