Deterministic Construction of Real-Valued Ternary Sensing Matrices Using Optical Orthogonal Codes

In this letter, a new class of real-valued matrices is presented for deterministic compressed sensing. A base matrix is constructed by cyclic shifts of binary sequences in an optical orthogonal code (OOC). Then, a Hadamard matrix is used for its extension, which ultimately produces a real-valued matrix that takes the entries of 0, -1 and +1 before normalization. The new sensing matrix forms a tight frame with small coherence, which theoretically guarantees the average recovery performance of sparse signals with uniformly distributed supports. Several example sensing matrices are presented by employing a special type of OOCs obtained from modular Golomb rulers.