基于过完备分析算子学习的图像超分辨率重建变分模型与算法研究

With synthesis sparse representation and joint dictionary learning, current image super-resolution (SR) approaches usually assume, either that a high-resolution (HR) patch shares exactly the same sparse coding of its corresponding low-resolution (LR) patch, or that there exists a linear regression relationship between the sparse codings of the HR-LR patch pair. Nevertheless, the unreasonability of those hypotheses will result in visually obvious artifacts while reconstructing some of the semantically remarkable LR image patches. To overcome the inherent disadvantages of existing SR methods, this project turns to a more advanced perspective of signal modeling, i.e., analysis sparse modeling. Specifically, a new structured analysis sparse model is proposed for image SR reconstruction via intensive study of overcomplete analysis operator (OAO) learning and nonconvex analysis sparse recovery. First of all, based on the nonconvex analysis sparse prior on image patches, learning a coherent seperable OAO is formulated as the semi-orthogonality constrained optimization. In the subsequent, based on the assumption that clustered similar LR and HR patches possess the consistent pattern of the analysis sparse representation, a structured analysis sparse SR model is constructed through joint OAO learning. Finally, via coupling the operator splitting and proximal gradient ideas, a fast reconstruction algorithm is deduced with an enhanced joint structured analysis SR model, obtained by seamlessly embedding the nonlocal self-similarity of natural images into the the structured analysis sparse SR model. To sum up briefly, the research in this project is of significant importance in both theory and practice, in that it will not only expand the regularization theory but also improve the reconstruction performance for the current sparsity-based SR approaches.

基于字典联合学习的图像超分辨率合成稀疏表示方法往往假设高、低分辨率稀疏编码之间完全一致或者具有线性回归关系。然而，对于某些语义显著的低分辨率图像块，既定假设的不合理性将导致重建图像呈现视觉明显的虚假效应。为从建模机理上克服超分辨率合成稀疏表示方法的潜在缺陷，本项目立足信号过完备分析稀疏建模理论，以过完备分析算子学习和信号分析稀疏重建为具体科学问题，探讨图像超分辨率结构化分析稀疏重建新模型与算法。首先，基于图像块非凸分析稀疏先验，提出半正交性约束优化的互相干可分离过完备分析算子快速学习方法；其次，通过挖掘高、低分辨率聚类相似图像块的分析稀疏支撑一致性，构建基于分析算子分类联合学习的超分辨率结构化分析稀疏变分模型；最后，通过耦合算子分裂和近邻梯度方法，设计图像超分辨率非局部结构化分析稀疏重建快速算法。本项目对于拓展超分辨率稀疏建模方法、提升超分辨率重建算法性能，具有十分重要的理论和现实意义。

基于学习的单幅图像超分辨率(Super Resolution; SR)是低层计算机视觉领域的基础性问题，同时是国际上备受关注的前沿性课题。本项目针对基于字典学习的单幅图像超分辨率方法存在着的两方面关键共性问题，按照“图像非盲超分辨率新型表示学习模型与算法”和“图像超分辨率新型非参数盲估计模型与算法”两条主线展开研究。在非盲超分辨率新型表示学习这条线上，本项目提出了基于Beta-Bernoulli过程的图像超分辨率卷积稀疏表示耦合学习模型、以及基于权重部分共享的超分辨率端到端多路深度卷积学习模型，逐步实现了非盲超分辨重建精度的大幅提升。在图像超分辨率非参数盲估计这条主线上，本项目提出了基于修正全广义变差（Total Generalized Variation）、以及Bi-L0-L2范数正则化的非参数模糊核估计模型，逐步实现了低分辨率模糊图像的鲁棒高精重建。在上述研究过程中，本项目还发现了图像盲去模糊与图像盲超分辨之间的天然联系，为此同时开展了图像非参数大尺度去模糊新型盲反卷积模型与算法的研究工作。在这条线上，本项目先后提出了基于非平稳高斯图像先验、以及基于多层贝叶斯图像稀疏先验自适应学习的图像盲去模糊模型，逐步实现了相机抖动等非参数大尺度模糊的鲁棒高清恢复。在图像传感器物理分辨率受限、摄像载体运动/抖动等诸多实际应用中，如视频实时监控、医学图像诊断、遥感影像探测、视频传感器网络等，本项目研究成果都具有重建高质量清晰图像的巨大潜能。对于具有模糊退化的低清图像，本项目方法无需人为假定模糊核的尺寸或类别，能够在较大尺度上自动估计退化图像的任意形状模糊核函数，进而实现（低分辨率）模糊图像的高精度（重建）复原。