Abstract: 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.

Key words: compressive sensing, measurement matrix, m sequence, spark