m序列压缩感知测量矩阵构造

Construction of the compressive sensing measurement matrix based on m sequences

利用m序列,提出了一种新的确定性测量矩阵构造方法,称为m序列矩阵.在压缩感知理论中,spark定义为测量矩阵的最小线性相关列数,是一个重要的性能参数,利用m序列的相关特性,推导了所构造测量矩阵spark值的一个下界.仿真实验表明,该方式构造的测量矩阵的重建概率明显高于同条件下的高斯随机测量矩阵;一旦给定m序列,则能确定出所构造矩阵的每一个元素值,避免了随机矩阵的不确定性;所构造矩阵具有循环特性,易于硬件实现,克服了随机矩阵浪费存储资源的缺陷,具有实用价值.

Sequence is an important pseudo random sequence with good correlation.A new method for the deterministic constructing compressive sensing measurement matrix is given through m sequences and called the m Sequence Matrix.In Compressive Sensing,the spark,the smallest number of linearly dependent columns in a matrix,is an important parameter to measure the performance of the measurement matrix.A lower bound of the spark of the proposed measurement matrix is given by considering its correlation.Besides,numbers of simulations show that the proposed matrix has much higher reconstruction probability than the corresponding Gaussian random measurement matrix.The elements of the proposed matrix are deterministic once the m sequence is given,which avoids the uncertainty of random matrices.And the proposed matrix with a perfect cyclic structure can make the hardware realization convenient and easy,which illiminates the storage space waste of random measurement matrices,thus having great potentials in practice.