基于信道编译码的压缩感知研究

This project focuses on the fundamental connection of compressed sensing and channel coding. By employing the fruitful results on the coding theory and techniques, various dual problems arising in the compressed sensing, including the construction of measurement matrices and the reconstruction algorithms, et. al, can be well addressed. Our research topics can be listed as follows. 1) Fundamental connections and dualities between measurement matrices and channel coding, reconstruction of sparse signals and channel decoding. 2) Application of channel coding and decoding over Galois fields for compressed sensing, with particular emphasis on the construction of measurement matrices and reconstruction algorithms.3)Compressed sensing in noise setting and redundancy parity-check matrices of channel coding.4)Compressed sensing with incremental measurements for sparse signals with unknown sparsity and rate-compatible channel codes. Hopefully, these researches will help to better understand compressed sensing from unusual view of channel coding, the fundamental connections between CS and channel coding will show their power on the design of measurement matrices and reconstruction algorithms for compressed sensing under realistic conditions.

本项目旨在通过深入研究压缩感知与信道编译码之间的内在关系，利用信道编译码理论和技术来有效解决压缩感知中的测量矩阵构造、信号重建算法等一系列问题。具体研究内容包括：1)寻求信道编码与测量矩阵构造，稀疏信号重建算法与信道译码之间的对偶性特征及基本约束关系；2)在可实现约束下借助于有限域上丰富的信道编译码理论和技术来解决压缩感知中的测量矩阵构造及信号重建算法问题；3)给出有噪环境下利用冗余校验矩阵来设计抗噪测量矩阵的设计规范;4)面向应用探求稀疏模糊信号基于递增测量的测量矩阵设计及高效迭代信号恢复算法。本项目的研究最终为通过信道编译码来理解和设计压缩感知关键技术提供必要的理论和技术支撑。

本项目主要研究了基于信道编译码的压缩感知技术，取得了一系列原创成果：1)针对整数稀疏信号模型以及现有整数压缩感知中测量矩阵硬件实现复杂、重构算法复杂度高等问题，提出了一种基于LDPC码的确定性测量矩阵构造方法及有效的整数信号重构算法，仿真结果显示，所提出方案的重构性能优于其他整数信号重构方案性能。2）针对二元稀疏信号，提出通过LDPC校验矩阵与FFT矩阵的克罗内克积来构造测量矩阵,然后基于该测量矩阵提出了一种Peeling解码算法用于稀疏信号重构。3）针对压缩感知中的PD（Peeling Decoding）重构算法在低信噪比下鲁棒性差的问题，提出了一种基于稀疏码的自适应压缩感知方法（ACSSG），在有噪声情形下，ACSSG方案的重构性能优于现有稀疏码的压缩感知方法，且其重构复杂度与现有方法相近。4）提出了一种基于Verification decoding (验证译码)和Interval-Passing（间隔置信度传播)的压缩感知算法。5）在基于信道编译码的安全机理方面，取得了一系列创新工作。