非线性稀疏表示理论及其应用研究

This project is to research the problem of non-linear sparse representation and its applications. Sparse representation has already been userd widly in natural signal process, yet its kernel ideology and processing objective can also be used in other domains. Based on analysis and conclusion of the limitation and problems to be solved of existing sparse representation method, the theory of non-linear sparse representation is proposed, mainly including:1) constructing the single objective non-linear sparse representation model, analyzing its characteristics and designing the solving algorithms to break through the linearity limitations of sparse representation theory in existence and extend its application domains; 2) constructing the multi-objective non-linear sparse representation model and designing the solving algorithms to make up the shortage of current sparse representation theory which can only deal with single-objective and to solve the problem of processing performance uncertainty in current model; 3) Combining the objective and solving procedure of non-linear sparse representation model to study the self-adaptive solving method for the model with unknown hyper-parameters and design the solving procedure for optimal performance of the model. The proposed theory and method will be applied in the domains including optimal configuration of TT&C resources and image construction based on parameterized model. The theory will be complemented by applications, as well as the applications will be extended through the theory. In a word, great breakthrough is expected in non-linear sparse representation model and its solving algorithm and the application areas will be extended. Therefore, the research has better theoretical and practical meanings.

项目研究非线性稀疏表示及其应用问题。稀疏表示在自然信号处理领域得到广泛应用，但其本质思想与处理目标也可应用到其它领域。在分析与总结现有稀疏表示方法局限与待解决问题的基础上，提出非线性稀疏表示理论，主要研究内容包括：构造单目标非线性稀疏表示模型，并分析模型性质与设计求解算法，突破现有稀疏表示理论的线性局限，扩展应用范围；构造多目标非线性稀疏表示模型并设计求解算法，改变现有稀疏表示理论的单一处理目标局限，并解决现有模型处理性能存在不确定性的问题；将处理目标与非线性稀疏表示模型求解过程相结合，研究模型超参数的自适应求解方法与设计模型最优性能的求解过程。在航天测控资源优化配置与基于参数化模型的图像重构领域对所研究的理论与方法进行应用，通过应用开拓理论，以理论扩展应用。项目在非线性稀疏表示模型与求解算法方面可望进行较大突破，并扩展应用领域范围，具有较强的理论与实际意义。

(1) 航天测控资源优化配置问题是研究如何在现有测控资源的基础上合理配置设备，使得测控任务需求既能得到满足，又能充分利用测控资源，即测控资源规模适当、布局合理，以较少的投入或测控资源获得较大的效益。将信号稀疏用于航天测控资源优化配置具有创新性，对这种方法具有促进作用，具有很强的研究价值。面向航天测控任务实际需求，通过对测控资源调度与优化配置中的优化目标和约束条件进行分析，研究建立了资源优化配置的稀疏表示模型。通过仿真产生了训练的样本，并利用K-SVD字典学习算法对模型进行了求解，得出了资源优化配置的方案。.(2)基于点散射模型与稀疏表示从参数估计角度研究多幅SAR图像超分辨成像模型与求解方法。针对目前SAR图像降质因素难以准确获得并参数化的现状，借助于点散射模型与稀疏约束，构造了类似于光学图像超分辨的变参数正则化模型。继而从最小化均方误差角度分析得到准最优模型参数的选择准则，从而实现了模型的自适应迭代求解。仿真实验验证了方法的有效性，得到综合多图数据可改善参数估计性能的结论，并将本文模型与最小二乘估计、广义岭估计的结果进行了详细的比较。.