基于渐进结构化学习的高维信息稀疏表示理论与技术

To meet with the rising demands on large-scale high-dimensional signal processing and transmission, we aim to propose the learning-based theory and algorithm optimized for high-dimensional signal representation, analysis and prediction by incorporating structured statistical learning and metric-based functional optimization. To be concrete, this proposal is to exploit the multi-dimensional topology of the input signal space to establish the optimal mapping between dictionary and sampled signals, so that the optimal signal representation based on structured sparsity can be achieved by exploiting the high-dimensional correlations derived by the multi-dimensional topology and investigating sparsity and low-rank property in original space. We also consider to construct the dictionary with progressive learning based on the multiscale analysis of featured structures and optimize it with parametric learning and stochastic sampling. Moreover, statistical predictive model is generalized to high-dimensional signals with nonlinear mapping under the constraints of structural coherence, in which graphical probabilistic models are leveraged to jointly optimize the predictive model over multi-layer relational network. In summary, we aim to propose the theory for sparse representation and high-performance prediction and develop practical analysis and coding techniques. Its theoretic achievements would benefit the ongoing research on compact representation and scalable processing of high-dimensional signals.

本申请利用结构化的统计学习和基于测度空间的泛函优化，致力于优化学习的高维信号表示、分析和预测理论，并建立应用系统。具体旨在分析高维信号的多维空间拓扑结构，建立字典和采样信号间的最优映射，充分利用拓扑结构衍生的高维相关性，探索多维空间稀疏性和低秩性，实现基于结构化稀疏的信号优化表示。研究内容包括：利用参数化学习和随机采样优化效率、基于渐进学习构建字典、优化面向公共服务平台的可伸缩信号处理。技术路线涉及：以特征结构一致性作为约束推演信号预测的统计模型，并通过非线性映射推广到高维信号空间；运用概率图模型，利用耦合优化建立多层次约束网络下的统计模型，形成高效预测和稀疏表示理论；建立实际的分析和预测编码系统。本申请自实际应用需求中抽象出科学问题，预期的理论和技术成果有助于高维信号可伸缩处理和紧致表示技术的发展。

为了适应日益增长的大规模高维信号处理与传输需求，本项目分析了传统信号处理理论和技术、结合结构化的统计学习理论和基于测度空间的泛函优化方法，提出高维信号基于优化学习的表示、分析和预测理论，并建立应用系统。主要研究内容为：（1）基于结构化稀疏的高维信号表示；（2）基于字典学习的高维信号表示；（3）基于结构化学习的高维信号预测。本项目3年来，共发表重要学术论文9篇，其中：SCI收录国际期刊论文5篇，包括IEEE Transactions顶级汇刊论文4篇，4篇本领域主要国际会议论文，参加了4次国际学术会议，作了2次国际学术会议专题演讲报告。