Research On Measurement Matrix For Compressed Sensing Based On LDPC Code

With the rapid development of science and technology, the requirement of digital signal processing is also increasing, however, the traditional Nyquist sampling theorem greatly limits the processing power of information. Meantime, the compressive sensing theory breaks the traditional sampling limitations, and transforms the sampling method from signal sampling into information sampling, which makes the small amount of sample data. Besides, we can use the sampling data which is much smaller than Nyquist sampling theorem required to reconstruct the original signal accurately or approximately. Compressive sensing theory mainly includes sparse representation, perception measurement and signal reconstruction, and perception measure is one of the very important parts. The constructions of Measurement matrix is the core content of sensing measurement, and its performance directly affects the implementation of compression and the accurate reconstruction of signal. At present, there is still no clear way to build such a matrix. How to construct a measurement matrix with better performance is the focus of this study.This study starts from the application analysis of Compressive sensing theory, analyzes the structure and the correlation from three parts of perception process, and provides the RIP conditions or non-correlation that should be satisfied by measurement matrix. Moreover, we have provided specific construction methods of commonly used measurement matrix on this basis, and have done simulation experiments in image signals to analyze and compare the performance of several kinds of measurement matrix. To solve all these commonly used measurement matrix while meet RIP conditions, but they are either too strong in randomness or too high in density, which leads to significant computation load and makes it difficult to achieve in the hardware; or that the simulation results are not very satisfactory.Aiming at the existing problems of measurement matrix, this paper studies the construction of measurement matrix from the following aspects: the sparsity of measurement matrix, and the difficulty of measurement matrix hardware implementation. Based on in-depth study of the measurement matrix, we found the parity-check matrix of LDPC code is kind of low density sparse matrix, which has strong sparsity. And during construction process, each of its sub-matrix is obtained by cyclic shift of other sub-matrices, so it is quasi-cyclic.Meanwhile, the parity-check matrix of LDPC code has strong orthogonality, theory proves that when the parity-check matrix of LDPC code satisfies RC constraints, there is non-correlation among its ranks, i.e., that means it satisfies the RIP conditions. Taking advantage of the above features of the parity-check matrix of LDPC code, we introduce the parity-check matrix of LDPC code into compressive sensing theory and construct a kind of LDPC code measurement matrix. Experiments show that the measurement matrix constructed in this paper has good observation effects, and the cyclicity of its constructure makes it easy to implement in hardware, it’s suitable to be used as measurement matrix of sensing measurement for compressive sensing theory.