Compressive sensing measurement matrix construction based on improved size compatible array LDPC code

ISC-array LDPC code matrix is evolved from SC-array LDPC code matrix to improve compressive sensing performance for large-size sparse signal. When q is a prime number, no repetitive row occurs in the shift index of SC-array LDPC code matrix, ISC-array LDPC code matrix performs comparably with SC-array LDPC code matrix. When q is a non-prime number, some repetitive rows will appear in the shift index of SC-array LDPC code matrix, which results in more 4-cycles and decreases the compressive sensing performance. ISC-array LDPC code matrix outperforms SC-array LDPC code matrix by effectively reducing or even eliminating the repetitive rows according to their distribution rule, 4-cycles are removed to the maximum extent. ISC-array LDPC code matrix qualifies for compressive sensing because of satisfying RIP well. It also has good quasi-cyclic structure and supports arbitrary code lengths. The simulations verify that the optimised ISC-array LDPC code matrix is advantageous in the image reconstruction quality, the robustness to noise performance and the algorithm complexity.