基于准循环低密度奇偶校验码的压缩感知测量矩阵

针对随机测量矩阵元素随机产生、不易于硬件实现的缺点,利用有限域上准循环低密度奇偶校验(QC-LDPC)码奇偶校验矩阵的构造方法,设计了一种确定性的结构化稀疏测量矩阵。由于QC-LDPC码的信道编解码性能较好,故以此为基础构造压缩感知(CS)测量矩阵预计有较好的性能。分别用一维和二维信号的CS重建实验验证新矩阵的性能,结果表明,与常用的测量矩阵相比,在相同的重建算法和压缩比条件下,新矩阵对应的重建误差较低,在峰值信噪比(PSNR)的评价指标上有所提高(0.5~1dB)。特别地,所提的确定性测量矩阵在结构上具有对称特性和准循环特性,如将其应用于硬件实现,可降低物理内存的需求量与硬件实现的复杂度。

Compressed sensing measurement matrix based on quasi-cyclic low density parity check code

Abstract: To overcome the shortcoming that random measurement matrix is hard for hardware implementation due to its randomly generated elements, a new structural and sparse deterministic measurement matrix was proposed by studying the theory of measurement matrix in Compressed Sensing (CS). The new matrix was based on parity check matrix in Quasi-Cyclic Low Density Parity Check (QC-LDPC) code over finite field. Due to the good channel decoding performance of QC-LDPC code, the CS measurement matrix based on it was expected to have good performance. To verify the performance of the new matrix, CS reconstruction experiments aiming at one-dimensional signals and two-dimensional signals were conducted. The experimental results show that, compared with the commonly used matrices, the proposed matrix has lower reconstruction error under the same reconstruction algorithm and compression ratio. The proposed method achieves certain improvement (about 0.5-1dB) in Peak Signal-to-Noise Ratio (PSNR). Especially, if the new matrix is applied to hardware implementation, the need for physical storage space and the complexity of the hardware implementation should be greatly reduced due to the quasi-cyclic and symmetric properties in the structure.