基于格型结构与CS理论的高效数字系统设计与实现研究

As the core of digital signal processing system, the study of design and implementation of digital system is always a very important research issue. With the help of the theories of matrix factorization, system structures, optimization techniques and compressed sensing (CS), design and implementation of digital systems with robust low complexity are investigated in this project. The project consists of three parts. Firstly, according to the theory of system structures and mathematical analysis methods, the relationship between the robustness and simplicity is studied considering on the two classes of quantization errors, which can provide a theoretic guide for design of digital systems. Secondly, based on the lattice filter structures, the impact of discrete parameters representation is investigated and measurement function for performance distortion is developed. The modeling for structure-based discrete coefficient filters and the corresponding optimization method are also considered. At last, based on the theory of CS and its reconstruction algorithm, the strategy for digital filter design is explored. A new approach for structure-based digital filter design is proposed. By studying on the design of high-performance and low-complexity digital filter, this project will provide important theoretical basis and technical supports for low-cost applications and help to promote China’s economic development with the Green Technology.

作为数字信号处理系统的核心部分，数字系统的设计与实现一直以来是一个非常重要的研究课题。本项目拟以矩阵分解、系统结构理论、优化算法、压缩感知 (compressed sensing - CS) 理论及算法等工具，对高鲁棒简洁数字系统的设计与实现进行研究，主要内容包括：1）依据系统结构理论和数学分析方法，结合考虑两类量化误差，研究数字系统鲁棒性和简洁性的内在联系，为不同类型的数字系统设计提供理论指导。2）针对格型滤波器这一类特殊结构，深入研究参数离散表示对整个系统的影响，建立滤波器性能失真的测度函数；同时以系统结构理论研究参数离散化建模及其对应的离散优化方法。3）基于CS理论及其重构算法，探索数字滤波器设计的新策略，提出基于结构的数字系统设计的新方法。本项目通过对高性能低复杂度的数字滤波器研究，为工程应用的低成本化提供理论支持和技术方案，以绿色科技为支撑促进我国经济的发展。

作为数字信号处理系统的核心部分，数字系统的设计与实现一直以来是一个非常重要的研究课题。本项目采用以矩阵分解、系统结构理论、优化算法、压缩感知 (compressed sensing - CS) 理论及算法等工具，对高鲁棒简洁数字系统的设计与实现进行研究，并对其他领域进行拓展研究，主要内容包括：1）依据系统结构理论和数学分析方法，设计了高性能低复杂度的格型数字滤波器；2）从实际应用的角度考虑，设计了一种并行处理的高效数字滤波器；3）CS理论及算法部分，将构造的等角紧框架用来设计鲁棒型测量矩阵，在同时考虑稀疏表示误差的情况下，应用于图像压缩场景，并取得很好的重构效果；4）相关其他领域的拓展，包括超启发式算法在车间调度作业中的应用、数据可视化等。本项目通过对高性能低复杂度的数字滤波器研究，为工程应用的低成本化提供理论支持和技术方案，以绿色科技为支撑促进我国经济的发展。