Research Of Deterministic Measurement Matrixs Based On Convolutional Compressed Sensing

Since its appearance, compressed sensing has attracted the attention of many researchers by virtue of its theory advantages. The core thought of this theory is to compress a sparse signal and take sampling, then reconstruct the original signal using a few measurements by suitable reconstruction algorithm. The theory includes three aspects:signal sparse representation, construction of measurement matrix and signal reconstruction algorithm. In this paper, we mainly launch the research in the construction of measurements matrix.First, we briefly introduce the compressed sensing fundamental theory. Then several commonly used signal reconstruction algorithm and measurement matrixes are compared with simulation experiment analysis, which lay the theoretical foundation for later research work.Second, the theory of deterministic measurement matrix construction based on convolutional compressed sensing is introduced. Based on this theory, a measurement matrix can be constructed by convolving the signal of interest with a filter and then subsampling. In this paper, based on convolutional compressed sensing theory, we construct several kinds of deterministic measurements matrix, which have been put forward before. These measurement matrixes include the operator constructed by m-sequence, the operator using Golay sequence and the operator constructed by FZC sequence. The simulation shows that the proposed matrixes can be used in CS signal reconstruction and easier for hardware implementation comparing with Gaussian measurement matrix. But the propsed deterministic measurement matrixes are complex-value matrixes, and the reconstruction performances are influenced obviously by the subsampler used in construction, which will limit the application of the proposed system.In order to achieve better reconstruction performance, we construct another kind of deterministic measurement matrix using Legendre sequence based on convolutional compressed sensing. The proposed operator can not only offer a full real-valued matrix, but also offer a similar reconstruction performance as that of Gaussian measurement matrix no matter the subsampling operator is random or deterministic. Besides, the proposed operator is easy to achieve and takes less time to complete the signal reconstruction.Based on the above research, in order to further improve the performance of the measurement matrix, some improvements are made based on the deterministic measurement matrix using Legendre sequence. Using the original Legendre sequence, a new kind of sequence named D-L (Decimated Legendre sequence) is constructed. We construct a new kind of measurement matrix using D-L sequence based on convolutional compressed sensing. It can not only offer a full real-valued matrix, but also supply an easier method for implementation. After many simulation experiments, it is verified that the proposed operator can offer a similar performance as that of Gaussian random measurement matrix for the signal which is sparse in time domain or frequency domain.