基于多维伪随机序列的压缩感知测量矩阵构造

Construction of Compressed Sensing Measurement Matrix Based on Multidimensional Pseudo-random Sequences

构造确定性测量矩阵对压缩感知理论的推广与应用具有重要的意义。源于代数编码理论,文中提出了一种基于多维伪随机序列的确定性测量矩阵构造算法。该算法选择迹表示函数产生二进制伪随机序列集合,并对其进行数值转换得到相应的双极性伪随机序列集合,此集合中的元素作为列向量进行排列即可组成文中的测量矩阵。理论分析和仿真实验表明,该方式构造的测量矩阵的重建性能优于同条件下的高斯随机测量矩阵。所构造矩阵可由线性反馈移位寄存器结构实现,易于硬件实现,具有实用价值。

It is significant to construct deterministic measurement matrix for the promotion and application of the compressed sensing theory. Originating from the algebraic coding theory,this paper presented a construction algorithm of multidimensional pseudo-random sequences based deterministic measurement matrix. This algorithm first chose trace representative function to generate the set of binary pseudo-random sequence. And then,the generated set of binary pseudo-random sequence was output as the corresponding set of bipolar pseudo-random sequence by numeric convert. The elements of bipolar sequence set arranged itself to constitute the measurement matrix as column vectors. Theoretical analysis and simulation results show that the proposed matrix can obtain better reconstruction results than the corresponding Gaussian random measurement matrix. The proposed matrix can make the hardware realization convenient and easy by means of Linear Feedback Shift Register（LFSR） structures,thus having its practical value.