Computational ghost imaging based on Walsh matrix replication

The Walsh function system has orthogonal completeness and is widely used in signal processing, image processing and communication. In this paper, three kinds of Walsh matrices, Hadamard order, Walsh-Like order and Paley order, are derived by Kronecker product based on row and block replication techniques of Walsh matrix, and the structural characteristics of different matrices are compared and analyzed. The generated Walsh matrix is used as the measurement matrix to modulate the optical field of the computed ghost imaging system. The simple binary object and the complex gray object are used as the target object, and the second-order correlation operation is used to reconstruct the target object. The numerical simulation results show that the three matrices can reconstruct the target object with high quality under full sampling conditions, but the reconstructed image quality of Paley-ordered Walsh matrix is much better than Hadamard order and Walsh-Like order under low sampling conditions, which can effectively reduce the data sampling rate and improve the signal-to-noise ratio of ghost imaging system.