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.