Research On Deterministic Measurement Matrix And Restricted Isometry Property For Compressed Sensing

Compressed sensing(CS) is a novel signal sampling theory. This technology employs a special sampling method, so there are wide application prospects in the areas of wireless sensor network, medical image processing, radar image and so on. CS breaks through the traditional Shannon-Nyquist bandwidth restriction on the sampling rate, by means of the non-adaptive measurements with a well below the Shannon-Nyquist sampling frequency and optimization methods, reconstructs signal with high probability.The measurement matrix construction is the key point that most researchers focus on. This paper focuses on the study of measurement matrix and the major works as follows:1. Sparse random matrices have attractive properties, such as low storage requirement, low computational complexity in both encoding and recovery, easy incremental updates, and they have attracted wide attention. This paper introduces a class of sparse random matrices. The restricted isometry property is an effective method to judge whether a matrix can be used for CS. To this make sure sparse random matrices can be used as the measurement matrix, the restricted isometry property of such matrix is proved in this paper.2. In compressed sensing, the sensing matrix plays a significant role in data sampling and reconstructing signals. It’s a hot and difficult problem to design good matrix which is efficient and easy to implement on hardware. This paper introduces toeplitz matrix and ciuculent matrix construction methods based on good pre-random property of chaotic system. Measurement results of one-dimensional and two-dimensional signals using the chaotic teoplitz and circulant measurement matrix are studied and are compared with the results of common random Gaussian matrix. Simulation results show that comprehensive performance of chaotic matrixes are better than Gaussian random matrix.