非线性稀疏表示理论及其应用

Non-linear Sparse Representation Theory and its Applications

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,主要包括:构造单目标非线性稀疏表示模型,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只能处理单一目标的局限,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,设计模型最优性能的求解过程。探讨了航天测控资源优化配置问题的非线性稀疏表示模型的构造方法。

The theory frame of non-linear sparse representation was proposed, based on analysis and conclusion of the limitation and problems to be solved of existing sparse representation method. The main contents include contructing the single objective non-linear sparse representation model, analyzing the solution characteristics and designing the solving algorithms to break through the linearity limitations of sparse representation theory in existence and extend its applica- tion domains; constructing the multi-objective non-linear sparse representation model and designing the solving algo- rithms to make up the shortage of current sparse representation theory which can only deal with single-objective and to solve the problem of proaessing performance uncertainty in current model; combining the objective and solving proce- dure 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 applying method was dis- cussed taking the optimal configuration problem of TT＆C resources.