Research On Constructions Of Deterministic Measurement Matrices Based On Sequences And Coding

Compressed sensing is an important signal processing technology,which has been widely used in medical imaging,radio astronomy and other fields.The theory is not bounded by the traditional sampling theorem,it unifies sampling and compression,and can completely restore the original signal with a very small amount of samples,saving a lot of space and avoiding unnecessary waste of resources.The research on measurement matrix construction is one of the key technologies in the field of compressed sensing.The random measurement matrix not only needs to store a large amount of data and takes up too much storage space,but also needs higher requirements for hardware configuration since it is randomly generated.In order to adapt to actual needs,the research of deterministic measurement matrices has been widely concerned.In this thesis,based on sequence and coding,the construction methods of measurement matrices are studied.Firstly,the deterministic measurement matrices are constructed based on the binary m-sequences.Codebooks are constructed by extracting rows from Zadoff-Chu matrices according to row index sets obtained from binary m-sequence structures at first,then measurement matrices are generated by converting codebooks as columns.Through the comparison of simulation experiments,the performance of the new measurement matrices is better than that of the random measurement matrices,and it is easier to implement in hardware.Secondly,the deterministic measurement matrices are constructed based on the MWBE codebooks.According to the constructing of measurement matrices based on codebook,two kinds of deterministic measurement matrices are constructed by using the quadratic difference set MWBE codebook and MDS codes respectively.Two new measurement matrices are obtained by transposing the codebook vectors through a specific mapping relation and replacing the elements in the matrices correspondingly.Since the MDS codes have a smaller alphabet set,the resultant measurement matrices have lower correlation and are easier to meet the RIP characteristics.Finally,the deterministic measurement matrices are constructed based on the set of frequency-hopping sequences.The two new measurement matrices are obtained by nesting the DFT matrix to the extended and binary base matrices,where the base matrices are obtained from two sets of one-coincidence frequency-hopping sequences.This method makes the measurement matrices more flexible in the selection of dimensions,while ensuring their sparsity,and provides more options for constructing the measurement matrices.